Monday, September 1, 2014

Devaluing Labor - Now As Never Before

A week ago, a talking head on CBS Nightly News observed - after extolling the spiking stock market - that the average American's wages have declined by a full 5.9 percent since 2000. When anchor Scott Pelley asked Ms. Schlesinger how the economy could fully recover if workers, people didn't have adequate income to purchase corporate goodies - she had no answer. (She also admitted that rather than create jobs the corporations were using money to buy back their own shares and enhance their profits by "automating" to increase share value.)

On this Labor Day, 2014, it is well for us all to ponder then, irrespective of our place in the labor constellation - whether employed or not - how we came to the sorry pass of American Labor being so devalued. One only needs to do the most rudimentary research to ascertain how far we've fallen since 1973-74. By one measure, as reported by Barbara Ehrenreich ('This Land is THEIR Land', p. 23),  one of her most popular books:

"the share of pre-tax income going to the top 1 percent of American households has risen to 16 percent. At the same time, the share of income going to the bottom 80 percent has fallen by 7 percentage points."

But it's worse than that! Those top 1 percent of people and indeed the top 5 %, have made out like bandits since the Bush tax cuts were passed in 2001, then extended (with the help of Neoliberal democrats) in 2011. As a result, there has been an average transference of $7,000 every year from lower and middle income earners to the top. According to a New York Times piece cited by Ehrenreich: "It's as if every household in the bottom 80% is writing a check for $7,000 every year and sending it to the top 1 percent".

How the hell did things get this bad for middle and working class labor? How has it come to be that now there is such a massive retrenchment of high benefits - high value jobs, while low value service jobs become the norm? It has been a long time coming, but numerous processes were at work, a few of which I will enumerate below:

(1) Cutting employee benefits, i.e. health plans - even after employees have retired with them.

(2) Eliminating defined benefits plans, such as provided standard corporate pensions - in favor or defined contribution plans (such as 401ks) in which workers are in it for themselves to accumulate adequate savings for retirement.

(3) Cutting wages - either de facto, or through eliminating the unions which protected them (much exacerbated after Reagan ascended to power)

(4) Firing/downsizing workers just before their retirement dates, so the company is free not to have to pay retirement plan benefits, or provide stock options, as per contract clauses.

(5) Re-engineering the workplace to increase its automation factor in order to dump workers, so increase profit margins by not having to pay benefits, etc.

(6) Shipping as many jobs as possible overseas, to places like Bangalore or Beijing, with labor costs barely 20% of what they are in the U.S. and no benefits to factor in.

(7) Firing - downsizing workers after mergers dictated by Wall Street interests, in order to enhance a company' profits through higher Wall Street share prices.

(8) Identifying older (over 50) workers as 'surplus' so that they can be replaced with younger workers for whom half the wages (or less) can be paid, with fewer benefits. (A recent 5-4 Supreme Court ruling a few years ago exacerbated this by asserting anyone claiming "age discrimination" could not file a suit in standing if that was the only charge)

(9) Eliminating nearly all permanent jobs which carry health and pension benefits, in favor of using 'temping', 'outsourcing' or some other device not requiring benefits. On the academic (university) front, using 'adjunct' professors, hired on a per hour, per course basis, without benefits., and with no possibility of 'tenure'.

(10) Tying health insurance to employment, so that when let go or fired, workers are waylaid again by having to do without critical protection. Thereby driving them into bankruptcy and-or poverty if they should get seriously ill or seriously injured in an accident.

All of these together, in concert, have forced a massive marginalization of the workforce. It is so disagreeable and extensive that it evokes the powerful words of Charles Reich in his book, Opposing the System,p. 22:

"We have built a machine for dehumanization of such force and destructive power, thorough its accumulated assaults on human dignity, that we are creating kinds and degrees of damage to human beings beyond anything ever known, with totally unforeseeable consequences "

And indeed, when one observes workplace killings, especially in the wake of firings - one gets a glimpse into these consequences. Not to say the fired people were "entitled" to get off this way, but that the system of American work itself has so regressed them that they are no longer able to see clearly what their choices are, in situations of desperation.

And don't think for a moment the military is free from this. As I tracked one of the charities to which I consistently donate, I found their main beneficiaries were families on U.S. military bases. That charity was primarily responsible for trucking in loads of free food from pantries to the bases - making the spectacle of military poverty high profile (especially following 9/11 when all entering vehicles had to be stopped for searches outside bases).

As Ehrenreich also noted from her book (p. 61):

"Market forces ensure that a volunteer army will necessarily be an army of the poor. The trouble is that enlistment doesn't do a lot to brighten one's economic future".

She goes on to say that the average pay for frontline battle troops (at the time of writing, ca. 2008) was $17,000 a year- "which puts them at about the level of theater ushers and crossing guards". Even 2nd lieutenants only earn an average of $26,000 - "less than most pest control workers and shoe salesmen". Yes, they do get benefits, but these enable families to barely keep heads above water. Also, as Ehrenreich notes, many service men and women have had to use credit cards to purchase kevlar or other protective vests because the Army couldn't afford them.

What kind of nation is this? One in which the labor pool has been nearly totally devalued and debased.

Probably no truer a statement ever appeared than barely 12 years ago, in an issue of Psychology Today no less (July/August 1998, p. 10. Includes graph):

"Starting in the mid-1970s, the nation's quality of life parted company with its wealth, and the gap between social health, and GDP is now bigger than it's ever been."

A graph of 'quality life indices' vs. GDP (ibid.) shows the measured divergence. It also suggests that we are a much sicker society than anyone imagined. The marginalization of the workforce, is surely one major barometer of that. The GINI coefficient, and research disclosing how it portends social and economic disintegration, is another. And bear in mind this awareness was at least ten years before the massive financial meltdown in 2008, which now has 16.7 million out of work and nearly 26 million under-employed. Meanwhile, corporate America continues to sit on a heap load of $867 billion in cash reserves rather than create jobs.

They won't add jobs until "demand rises"- which means consumers buying more. But consumers are keeping their wallets tightly zipped up because they're still de-leveraging out of debt which, as recently as 2007, saw them with an average of $1,400 of liabilities over assets.

Cynical aspects of even remotely trying to reach full employment in the U.S. are seldom mentioned. For example, that a deflationary impetus has been a prime influence in companies cutting back on work forces, because the employment cost is too prohibitive. (Or, using 're-engineering and re-tooling to replace workers with robots or self-service queues such as at many supermarkets now)

Also, the cost of keeping people employed is seldom mentioned. But, the Federal Reserve even has a statistic to keep track of it: "the Employment Cost Index." It is basically, a per capita index of how much cost is attached to keeping each unit of workers in jobs. This includes benefits, as well as wages and salaries, including overtime pay. The higher this index, the greater the number of employed people. The lower, the more unemployed. Market specialists and strategists do NOT want employment rates high because they inflate the Employment Cost Index, and also:

"Inflation fears are especially acute ..because unemployment is too low. When available workers become scarce, employers must often bid more for their services and then raise consumer prices to make up for higher costs." (The Baltimore Sun, p. 1E Jan. 27, 1997, 'Employment Cost Is a Hot Number').

To put this all in more blunt terms:

Economists and Wall Street investment firms have learned that for roughly every 1.3 million people out of work, inflation decreases by 1%. (And the Employment Cost Index, though not necessarily by the same amount).

They also know(as the Federal Reserve Corporation does) that low inflation increases stock prices - which makes more money available to business (though not to their employees, since profits are always invested in new capital - i.e. issuing more shares, rather than labor). The end result is that there is an enormous impetus to eliminate as many good jobs and workers as possible - to maximize a company's stock prices, and enhance capital.

In other words, capital is opted for over labor, and this was the topic of The Judas Economy: The Triumph of Capital and the Betrayal of Work, by William Wolman and Anne Colamosca.

The point is then, that labor is devalued precisely because we live in a "Judas Economy" where capital is revered over it. One of the most disgusting indices as the authors note, is that productivity in relation to GDP has increased more than 40% in the interval since 1973 even as wages-salaries have remained almost stagnant. Of course, one major reason is how "greater productivity" is attained. Often by firing a number of workers and ditching their benefits, and making the remaining force do their work plus that of the downsized ones. OR- tossing out 80% of a workforce and replacing them all with automation.

So much for labor and Labor Day!

Americans, the kings of Bullshit, do a good job of talking it up and pretending like the nation extolls its regular workers. In truth, it disrespects them and the sure sign is how the trade unions have been treated and dismissed since the Reagan era. I leave with Barb Ehrenreich's powerful words (pp. 6-7):

"How many 'wake up calls' do we need, people? How many broken levees, drowned cities, depleted food pantries, people dead for lack of ordinary health care? (Waters poisoned by blown deep water oil wells)......Why don't we dare say it? The looting of America has gone on too long, and the average American is too maxed out, overworked, and overspent to have anything left to take. We need a new deal, a new distribution of power and wealth, if we want to restore the beautiful idea that was America".

A start can be made by increasing all Social Security benefits ASAP - so people can reap back in social insurance benefits what they failed to get in fair wages. Yes, the increase in benefits needs to be across the board and at least 6 %. Cuts that are guaranteed to only cause the gulf between capital and labor to grow even more. Instead of keeping those, cuts - take $2.2 trillion out of it to rebuild our decaying and crumbling infrastructure while also putting tens of thousands of people back to work....with full benefits!

Saturday, August 30, 2014

Bloggers Are More Opinionated Than FaceBook Users? They Have To Be!

As reinforced once more, we learn that those who use Facebook and Twitter are of a different species from those of us who blog. The latest research discloses they're "much less opinionated" - to which I respond,  'DUH!" Of course they are! Facebook as well as Twitter are venues for social schmoozing and sharing slices of life,  not providing political opinions that can be polarizing:  upsetting your virtual or real friends, as well as family. So people using Facebook would naturally tend to keep opinions to themselves as opposed to publicizing them,

Now a Pew Research Report released Tuesday validates this. The Report found that those who use Facebook and other social media sites are much less likely to share personal opinions, even offline. These findings run counter to how many view social media - which is basically as a bunch of self-opinionated, solipsistic blabbermouths. In truth, they are more likely to blab about minor social engagements, parties they went to or special trips - while posting photos and jokes  - as opposed to giving negative reviews of Obama or Obamacare or discussing Ferguson or Snowden..

In a specific case, to do with NSA whistle blower Edward Snowden, 1,800 social media users were asked their opinions.  Researchers noted a "spiral of silence" to do with any opinions - meaning the FB and Twitter users were more likely to "clam up" - as well as shy away from going near any hot button issues. This in total contradistinction to those of us who blog and believe our mandate is to inform about critical issues - including government mass surveillance, fracking ravages and climate change - and not keep silent.

Those of us who blog then are born with opinions and let's face it, to blog you HAVE to be opinionated! If you don't have opinions about any and every thing then you will likely be a dead end blogger running out of ideas after ten posts. Also, a boring one at that - mainly posting accounts of the last turtle race you observed on a beach or another kitty - doggie boxing match.  All stuff that could easily go on FB.

The bottom line? For those who use Facebook and Twitter, there is a much greater social  comfort level with "ice bucket" challenges than political banter and exchanges. Which suits those of us who blog just fine, because the person who wants some spice with his or her information will seek out our virtual spaces rather than FB or Twitter. They will then see our (often) singular opinions about one issue or another and in addition, see how we reason our justifications, say on why we don't find the "ice bucket challenge" all that cool.

Another Pew finding: The typical Facebook user - say who logs onto the site a few times a day -  is half as likely to discuss Snowden's leaks as a non-FB user.  Twitter users, those who cut their communications to 140 characters or less, are one fourth as likely to discuss Snowden. In a way this ought to be obvious given that any dummy can see the space allotted to discuss topics at length - in FB or Twitter - is much reduced from what a blog provides - which is why we opinionated types don't use FB or Twitter to offer our takes.  Those who do use them are "hesitant to speak up for fear of starting an argument or losing a friend."  And they ought to be, because it's not the right venue!

One  communications professor, Keith Hampton, has this take:

"A society where people aren't able to share their opinions openly and gain from understanding alternative perspectives is a polarized society."

Maybe, prof, but there are also right and wrong venues to share those opinions, and maybe the FB and Twitter users get it. If they really want to share they can BLOG!

Friday, August 29, 2014

Burger King's Greedy Move Betrays the U.S. and Its Customers

The news that BURGER KING - home of the 'Whopper' - could be moving to Canada, where its taxes would be paid, has many long time customers (including your truly) upset. Already, by Monday afternoon,  social media exploded with disapproval with over one thousand negative comments on BK's Facebook page. According to one customer, Shawn Simpson, interviewed outside a BK in NYC:

"For them to take their headquarters and move it across the border is a negative to me."

He added that he "didn't like the idea of the company paying its taxes to another country."

Well, me neither!  Since it was established in 1957 in Miami, I have been a Burger King customer - not on any frequent basis - like eating there three times a week - but more like once a month. I always preferred the taste of the Whopper to the Big Mac and the best Whopper I've ever eaten (and wifey too) was at a BK on Picadilly Circus, London in July, 1978.  Some of my first malted milk shake and burger dates were at the Burger King in Miami located near the Palmetto Expressway and NW 42nd Ave.

So it is disheartening now to learn this news, almost like a betrayal. Some financial gurus have proclaimed that "it's rational" and even the great Warren Buffet has bought a bunch of new BK shares, though once proclaiming that no CEO ought to escape more taxes than his workers. Cognitive dissonance anyone?

If Buffet were serious regarding his salary and tax proclamations, he'd have dissed the move - which took no cognizance of workers and merely exploited mammoth loopholes in current tax legislation. But then, despite all his blabber, Buffet is a Wall Street investor and all that counts is share price. Let's hope with all the taxes now saved Burger King will do the right thing and at least give its workers a raise!

Here's the skinny: Burger King currently earns about $1 billion a year but its customers aren't buying like they used to. Mickey D's still leads them, but let's face some hard facts: people now have many more choices including antibiotic -free fare at Chipotle's and also there's the general trend to healthier food choices. It is thus unrealistic to expect most people to go to the King as often as even twice a week. The last Whopper I ate (actually two) was about a month ago and that was via a coupon where you got one free with the purchase.  (I more often go to get breakfast, a sausage croissanwich and small black coffee).

Burger King also pays $51 million a year in corporate taxes and that's where they want to try to make a tax cut. They believe that by anchoring operations in Canada (via buying out the Canadian coffee and doughnut chain Tim Horton's ) they can cut taxes nearly 30% while also creating the 3rd largest fast food restaurant. But is bigger always better? Actually no! Ask MacDonald's,  which has seen steady losses over the past couple years mostly due to competition from the likes of Chipotle's and Panera Bread but also from the greater health consciousness of consumers who now often eat at home.

Thus, merely jumping to a Canadian tax base via a takeover is not likely to help BK long term.

Meanwhile, Burger King spokesman, Miguel Piedra, claims that while the new headquarters will be in Canada, Burger King would still continue to be run out of Miami. That's some consolation, but not much.

Here's the nasty thing about this tax inversion impetus, dozens of companies are now doing it (they say to cut costs) and are moving billions to offshore accounts.. And yeah, though the lazy corporate media report the U.S. has the highest corporate tax rate in the world, at 36% - the facts are substantially different.  While the on-paper tax rate is 36%,  the actual amount paid by the typical corporation is 12 1/2 percent. Which effective rate is really among the lowest in the world.

Part of the reason for this aberration is that Uncle Sam himself "has allowed companies the right to write off 100% of the purchase price of new equipment in 2010 and 2011". (According to one report from TIME< in Feb. 2012) This was done to theoretically "spur investment and create jobs". One wonders then how come these companies are still sitting on almost $1.5 trillion and are doing little to create more jobs. They'd rather use the $$$ to buy back shares. (Let's keep in mind here the population replacement rate for jobs is nearly 180k a month, i.e. the number required to provide steady, full time work to new monthly labor force entrees  - and we still have some 4.5 million jobs to make up that were lost after the 2008 financial crisis.)

Whatever the reason, the engineered corporate tax avoidance has had a dunning effect on our society along with the top 1% escaping their own fair tax assessments. According to TIME (ibid.), corporations account for only 9% of the nation's tax bill compared to 40% in 1943. That means citizens are now left to make up that difference, and the ones who are happen to be in the lower quintiles of income - even as the upper 5% have seen their wealth soar.

This means that more companies using the ruse of tax inversion will create even more tax burden on the rest of us by virtue of abdicating their own responsibilities. The most misplaced aspect is how the corps that do this now have over $150b sitting offshore in accounts while the U.S. scans the offshore accounts of private citizens - which are usually pitiful by comparison. (Citizens with offshore accounts must report each having more than $10,000 in it, on a FATCA form.)

So, basically, the corporations are allowed to get away with tax avoidance 'murder' while very strict oversight laws now apply to private citizens.  No surprise then that President Obama and Congress have criticized tax inversions because they means a loss of tax revenue for the U.S. government. So why not DO something about it then? Where is the political will to act if neither likes it?

Most likely because they are terrified of pissing off Wall Street. The proof? Burger King's stock surged $5.78 a share or up 21 percent on Monday to $32. 89. Once more, Wall Street rejoices like it does when higher productivity gains come at the expense of having fewer workers do the jobs of every two laid off. And as they do by awarding higher share prices to airlines that employ "densification" - stuffing ever more people into aircraft cabins to maximize profit! Our nation, sadly, is still hostage to Wall Street.

See also:

http://www.smirkingchimp.com/thread/dave-johnson/57890/now-burger-king-renouncing-u-s-citizenship-lets-eat-somewhere-else

Solutions to Quantum Mechanics Problems (2)


1) We see that from the diagram below that  if L = 3 we get one values for . and three for j :

Phil Stahl's photo.

So 1 = 1 and 2 = 2 therefore:  1 + 2 = 1 + 2 = 3.

Meanwhile, S can be defined by only one value of s, or s = ½

The possible j-values are:

j =
+ s = 1 + s = 1 + ½ = 3/2

j =
2 +s = 2 + ½ = 5/2
j = - s = 1 - s =  1 - ½ = ½

j =
2 - s =  2 - ½ = 3/2

So in total: j = ½, 3/2 and 5/2

Note that, conforming to j-selection rules, all the j's differ by an integral amount, though they are half-integral (e.g. 3/2, 5/2) themselves.

To obtain any J (total angular momentum) we need an L-S coupling vector that yields J = 5/2. Two possible L-S couplings are available: [L + S] and [L + S – 1] and it is the last that yields the appropriate result: [3 + ½ - 1] = 5/2

This means we need values such that 
1 = 1,  2 = 2 and s = ½ to make this work.


2) The vector solutions (which the reader can do) following the same tack as the previous probme, will show:

j =
+ s = 3 + ½ = 7/2

and:

m
J  = -7/2, -5/2, -3/2, -½, ½, 3/2, 5/2 and 7/2

meanwhile:

j =
- s = 3 -  ½ = 5/2

So:

m
J = -5/2, -3/2, -½, ½, 3/2, 5/2

Note that these last m
J quantum numbers would also be the ones applicable to the original problem for which: L = 3 , S = ½, and J = 5/2.

3)  a) The numerical value of the total angular momentum is given by:

 
L = [ ( + 1)]1/2 (ħ)

Where = 3, then”


L = [3 (3 + 1)]1/2 (ħ)  =    [3 (4)]1/2 (ħ)   =   3Ö2  ( ħ)

b) The z-component of the orbital angular momentum is given by:

 
L(z) = m ħ

For this election,  m   = 3, so that:

 
L(z) = 3 ħ

(4) We have ℓ1 =3 and ℓ2 = 2, then:

Therefore, the possible values of L will be found  from letting ℓ1 =3 and adding each next descending value of m   from 2, to 1, to 0, to -1, to -2:


(3) + 1 =   4


(3) + 0 = 3

 
(3) + (-1) = 2

 

(3) +  (-2)  = 1

 
So the total angular momentum L can have the values:

5, 4, 3, 2 and 1.


The f electron has ℓ =3  so that the total angular momentum quantum number possibilities are:


j = ℓ + ½,   ℓ - ½


Then: j = 7/2,  5/2


(5) For 4s 3d we have:

1 = 2, s1 = 1/2, 1 = 0 and s1 = 1/2. Then for the maximum value:

 
1 + 2 = 2 + 0 = 2

and: s= s1 + s2 = 1/2 + 1/2 = 1

The lowest  energy level is then:

 
4s 3d (3D1)

 
Since 2s' + 1 = 3, leading to minimum:


j' = [s' - '] = 1.

Using the assorted combinations, for
'= 0 and ' = 2, to get the respective j' values (in combination with s' = 0) and then further for s' = 1, we arrive at the energy configuration diagram shown below:
Phil Stahl's photo.

 

 

Thursday, August 28, 2014

An Introduction to Quantum Mechanics (2)


2.  Electron Spin and the Stern-Gerlach Experiment

So far, we've seen three different quantum numbers: n (principal), (angular momentum), and m (magnetic). We now examine how the fourth quantum number (ms) or electron spin came about.

By the early 1920s, quantum mechanics had developed to the point that theorists realized an electron magnetic moment ought to exist. In any external magnetic field B, the magnetic moment ought to experience a force similar to what a magnetic compass needle experiences in Earth's magnetic field. According to quantum mechanics, the assumed values should be quantized, so the magnetic moment can assume only certain values, given by:

2
+ 1

Thus, the orientation number will depend on the second or azimuthal quantum number,
. The total angular momentum (L) would therefore be:

L =
ħ  [ ( +1)]1/2


    In 1922, the German physicists Otto Stern and Walther Gerlach passed a beam of electrons through a non-uniform magnetic field B as shown in the top sketch of the diagram (C denotes collimator and D, detector plate). A non-uniform field meant the field was stronger on one side of the beam than the other. As predicted from theory, the force on the magnetic moment of the electrons is such that the field ought to deflect the beam according to the orientation of its moment.

   The field should therefore split the beam into 2
+ 1 parts (according to 2 +1 orientations). Stern and Gerlach found their beam of hot silver atoms split into two parts. At first this appeared surprising and at odds with theory but later work showed the conflict could be resolved if the electrons going into the opposing (up and down) beams, had their own spins, or intrinsic angular momenta.

Phil Stahl's photo.
 


Fig. 7. Illustrating the Stern-Gerlach Experiment.

In this case, the upper beam would feature electrons with "spin up" angular momentum of (+1/2) while the lower beam would feature electrons with "spin down" angular momentum of (-1/2) . These are shown at the lower section of the diagram. Note that in each case, spin up or down, the orientation accords with the direction of rotation: clockwise or anti-clockwise.

The refining experiment was actually done by Phipps and Taylor using a beam of heated H-atoms. They began by defining the magnetic dipole moment such that:

m z = - g() u B  m

where, as before, m
= -, - +1, 0, ....+

and u(b) is the Bohr Magneton: u B = eh/4
p m

where m is the mass of the H-electron.

Meanwhile, g(
) is known as the "orbital g-factor".

From their low oven temperature, Phipps-Taylor recognized that
= 0 for the electrons coming off and entering the magnetic field. Therefore, m = 0. Since this was so, then:

m z  = 0

Phipps -Taylor therefore assumed the beam would be unaffected or not split at all. Yet, it split into two symmetric components, e.g. deflected symmetrically, as shown in the graphic below. Given the earlier Stern-Gerlach experiment, plus their own, they therefore had to expect the electron had its own magnetic dipole moment..

They assumed this to be a spin magnetic moment 
m s, due to the electron having an intrinsic angular momentum S  analogous to L (angular momentum) so that:

S = [s(s + 1)]1/2  
ħ  and S z = m s (ħ)

 
Where S z   is the z-component of spin angular momentum

Then m
s is the electron spin or spin quantum number, 1/2 or - 1/2,

Then the electron magnetic dipole moment would be:

m s = - g(s) u B  / ħ [S]

To nail down the basis quantitatively, Phipps-Taylor knew that the net force felt by the electrons traversing the field would be:

F z = - (dB z /dz) u B  g(s) m
s

where m
s is the putative spin quantum number.

Since they knew the Bohr magneton u B = 9.27 x 10-24 J/T

and dB/dz could be measured (e.g. the difference in the B-field over the collimation width dz)


then :

g(s) m
s =  F z / - (dB z /dz) u B = + 1

as measured.

Since g(s) = 2, then by deduction:

m
s = +  1/2

Thus, Phipps and Taylor discovered that the splitting effectively showed two possible values for the orientational potential energy, or:

 
 D(E) = - m s B = +g(s) u B  B/2.

 
As an example, let's compute S for the value m s = 1/2.

S = [s(s+ 1)]1/2
ħ  = [1/2(1/2 + 1) 1/2 ħ  =

[1/2 (3/2)] 1/2
ħ  = [3/4] 1/2 ħ  =  (Ö3/2) ħ  

 
This result can be shown in diagrammatic form on a spin diagram, e.g.

 


Phil Stahl's photo.
Fig. 8. Illustrating spin quantization

 
Note in the diagram how the magnitudes for  S z   are first laid out on the vertical axis with lines drawn to a semi-circle, then the arrows are drawn to intersect with the  S z values  of + ½.

 
Example Problem: (See the Solution for Problem (2) from Previous set posted yesterday)

 
3. Space quantization and L-S Coupling:

 We now want to venture a bit deeper into the quantum mechanics of the hydrogen atom with a view to doing more elaborate problems, ultimately leading to tangling with what we call "L-S Coupling", or combining the orbital angular momentum, L, with spin angular momentum, S, to arrive at the J value.

For now we just want to focus on basic principles of angular momentum for classical physics. In terms of an orbiting planet, for example, we can specify the orbital angular momentum as:

L = m v r

That is, assuming a circular orbit of radius r, and a body of mass m, with velocity r, the orbital angular momentum will be L.

Now, what about at the atomic level? Bohr, in his Bohr model, visualized electrons behaving like tiny planets and orbiting a central nucleus. For the simplest atom, hydrogen, this meant one electron circling a single central proton. Bohr specified the rule for orbital angular momentum - using the principal quantum number, n, as:

mvr = n (
ħ)

where again, h is Planck's constant (6.6254 x 10 -34 J-s) and
ħ the reduced Planck constant.

However, this model failed to correctly predict the orbital angular momentum for the hydrogen electron, yielding a value of 1 unit, which is wrong. In addition, if L = 0 one would find the electrons oscillating in a straight line through the proton nucleus - which is impossible! Thus, it had to be modified. The modifications were possible once one removed the "planetary model" (which is classical and deterministic) and turned to the wave model. In this case, the orbital angular momentum assumes certain specific values such that:

L = [
( + 1)]1/2 (ħ)

(
= 0, 1, 2, ......., n-1)

In the above case, when
= 0 we find L = h/2p  = ħ  = 1. 054 x 10 -34 J-s

The fact L can be zero and is acceptable discloses why classical mechanical models fail at the quantum level.

Now, what if instead we have the angular momentum quantum number
= 2?

Then: L = [
( + 1)] 1/2 (ħ) =  [2(2 +1)] 1/2 (ħ) =  Ö6 (ħ)

and a set of allowed projections for L are obtained as shown in the  diagram (a) as well as orientations.


 

Fig. 9. Space quantization and the quantum number, L

 
Of particular interest are the allowed values for the vertical component of the orbital angular momentum vector, which we designate: L z. (L z is the projection of L along the z-axis and has discrete values, e.g. 0, h/2p  , h/p  , - h/2p  , - h/p  for the case given).

In general L z is specified according to:

L(z) = m
ħ

where m
is the magnetic quantum number.

 
The key point here is that the direction of the orbital angular momentum quantum number L is quantized with respect to an external magnetic field. We call this "space quantization".

Recall that m
 can range from - to , so for = 2, we have:

m
= +2, +1, 0, -1, -2

When we multiply each of these by (
ħ) we obtain the quantization of L z as depicted in diagram (a) of Fig. 9.

It should also be obvious to anyone who's taken trigonometry that one can obtain the angle between the vertical projection L z of the vector L, and L. ( See diagram (b) of Figure 9).

The angle (
q) can indeed be found using the cosine relation (adjacent over the hypoteneuse) which yields:

cos (
q) = L z  / L = m  / [ ( +1)]1/2

Of course, it ought to be self-evident that we are obtaining allowed values for the angle, since obviously m
is going to range from -2 to +2)

Thus, for the problem we've considered (with
= 2) we have the allowed cosines and angles:

m
= 0  so cos(q) = 0 so t = 90 deg

m
= 1  so cos (q) = 1/ Ö6 so q = 65.9 deg

m
= -1  so cos(q) = -1/ Ö6  so  q = 114.1 deg

m
= 2 so cos(q) = 2/Ö6  so q  = 35. 2 deg

m
= -2 so cos(q) = -2/Ö6 so  q= 144.7 deg

Question: Say an electron in an atom (e.g. hydrogen) has zero orbital angular momentum (
= 0) does that mean it has zero total angular momentum?

NO, because in quantum mechanics we find that for every electron in a given atom we have to process two kinds of angular momentum: orbital (L) and spin (S). Even if the electron experiences no precession or torque it must still exhibit a total angular momentum.

Earlier, we saw for the total orbital angular momentum:

L = [
( + 1)] 1/2  ħ  


We also saw that each electron has a spin angular momentum:

S = [s(s + 1)] 1/2  
ħ  

for which s assumes one or other of the electron spin quantum numbers, m
s = +1/2 or -1/2.

It can be shown  that S is always:        [3/4] 1/2  
ħ  

Now, we reckon in what we call the total angular momentum or J, such that:

J = [j(j + 1)] 1/2  
ħ  

and j =
+ s (note the common letters apply to different quantities than the capital ones!)

Thus, for an electron with zero orbital angular momentum (l=0) we have:

j =
+ s = 0 + 1/2 or + s = 0 - 1/2

so: j = +1/2 or -1/2

Then we have:

J = [j(j + 1)] 1/2  
ħ  = [3/4] 1/2  ħ  

for either j (which readers can also verify)

We can also find (as we did with L for Lz, the projection of the total angular momentum quantum number on the z-axis (Jz  ) which will be:

J(z) = m
J ħ

where m
J = -j, -j+1, ......+j

Readers with an intuitive grasp of vectors, or if they've worked with vectors - say in high school or college physics, will quickly see that the name of the game is to obtain a vector sum such that:

V = V(1) + V(2)

In this case, L plays the role of V(1), and S plays the role of V(2)

Then we obtain for J:

J = L + S

As any physics student knows, the way to obtain the vector sum is via the law of cosines and this is demonstrated in the diagram below along with the computations. This is for the case:

L = 3

S = 1/2

J = 5/2

and the angle (
q) can also be obtained as shown in the diagram below:

Note that in a weak magnetic in which the atom is situated, the L-S coupled system depends on j, in other words this very angle between the vectors L and S. Meanwhile, the orientation of the atom on the whole, depends on m
J.

 
With detailed descriptions using the quantum numbers and proper solutions of the Schrodinger equation, we can assemble a table of the respective numbers and the corresponding wave state solutions, e.g.

 

Another useful activity is to draw energy level diagrams using the given electron configurations for a particular atom. For example, consider the schematic energy diagram for the 2p 3s configuration for the carbon atom (12 C 6) with each level labeled  with spectroscopic notation:

Phil Stahl's photo.

In the 2p3s configuration, we know  =1 corresponds to p: so n=2, =1, m = +1, m s = + ½.   For the electrons in the 3s shell: n=3, =0, m = 0 and m s = ½ (and (- ½), for second).]

Each level of the diagram can then be sketched in, i.e. for the higher s-level s= s1 + s2 = 1/2 + 1/2 = while for the lower: s= s1 - s2 = 1/2 - 1/2 = 0. The j’s are found by taking the appropriate ℓ + s combinations, thus ℓ1 + s1 = 1 + 1 = 2, ℓ1 - s1 = 1 – 0 = 1 and so on.


Problems:

1) State which values of
, s, and j would apply to the case in the diagram, such that the assorted angular momentum vectors have the values identified.

2) Enumerate the possible values of j and m J for the states in which = 1 and s = 1/2 and draw the associated vector diagrams.

3) Consider an electron for which n = 4, = 3, and m = 3. Calculate:

a) the numerical value of L, the total orbital angular momentum

b) the z-component of the orbital angular momentum.

4) A two-electron atom for which the orbital angular momentum quantum numbers are ℓ1 =3 and ℓ2 = 2 can have what values for the total orbital angular momentum number L?  Determine the possible values of the total angular momentum quantum number of single f  electron.


5) For 4s 3d  configuration we have:

1 = 2, s1 = 1/2, 1 = 0 and s1 = 1/2.

 
Using the assorted combinations, for '= 0 and ' = 2, to get the respective j' values (in combination with s' = 0), and then further for s' = 1, sketch the energy configuration diagram

How the Frackers Prevailed in Colorado


Thanks to an extended report, we now know how Gov. John Hickenlooper, his Neoliberal Dem cronies and the fracker brigade managed to prevail in Colorado. By "prevail" I mean that they managed to finagle a closed doors, or back door deal - presented as a compromise  - that resulted in Dem rep Jared Polis removing his two local fracking initiatives from the November Ballot.  As the Post put it in its report ('Hickenlooper's Deal', p. 1A, Aug. 24):

"Nearly every person interviewed by the Denver Post doubted that anyone but Hickenlooper, a former geologist who has allies in the energy community and environmental communities,  could have pulled off a compromise."

But the problem is that it's no real compromise, only a puny token sham that managed to scrap actual potential for action. According to the Denver Post report back on Aug. 8:

"A 20 - person commission was announced Monday as part of a compromise to keep two oil and gas oriented initiatives from the fall ballot."

And what, pray tell, would  we see from this commission?

"The commission will have 6 months to make recommendations to the legislature which will then consider further legislation."

Oh, terrific! Six months to make "recommendations" and then the (bought out) legislature will have its say in making new laws. All you need to know is that the two largest fracking companies - from Texas- cheered wildly at the news. Can you figure it out now? Because never mind the legislature, the 6 month span will allow the drillers to put down 5,000 more frack wells, threatening our air, soil and ground water, see e.g.

http://brane-space.blogspot.com/2014/05/now-fracking-pollutes-soil-as-well-as.html


Anyway, Hick and his compadres were propelled to act to get a deal - any deal - after learning from Brian Lawrence (who founded Yorktown Partners - a company that invests in energy) that while the firm had planned to invest $1 billion in Colorado energy companies they were unable to proceed while any fracking control items were on the ballot. Thus the impetus for Hick to come up with any kind of bogus deal he could.

The breakthrough came when U.S. Rep Ed Perlmutter organized a dinner at a downtown Denver steakhouse to discuss the ongoing fracking debate and try to come to a resolution. No members of the fracktivists were allowed to attend, only the inside pols and their lackeys. Oh ...and the oil and gas representatives.  According to the Post (p21 A, ibid.):

"To Chris Castilian, director of government affairs for Andarko Petroleum and deputy chief of staff for former Republican governor Bill Owens, the dinner was a watershed moment."

Oh, I am sure it was as the weasels - in their secluded meetings-  found concordance on how to craft a deal to screw the public out of an opportunity to vote for local control of frack operations. Now, they're at the mercy of "commissions" and an industry-driven "task force".

To make a long story short, Hickenlooper according to the Post,  "practiced shuttle diplomacy" until he got all the participants on board as well as PR firms   - to be able to sell this sham to the public. After all, following all the hoopla of the ballot initiatives you had to toss them a rag when the measures were removed. (It helped of course that the state Dept. Of Natural Resources houses the Colorado Oil and Gas Conservation Commission - which is the industry 'pet' group designed to run interference on fracktivists )

As Hickenlooper beheld the "hangman's noose", i.e. the date of Aug. 4 approaching with all the signed petitions that would enable the two local fracking control initiatives, he and his minions pushed into overdrive to secure the bogus deal. The break point came when Polis caved under the pressure and dropped all additional demands concerning the composition of the task force designated to oversee the issues via the commission set up for the compromise. The road was then free and clear to bamboozle the public. (Polis was told if he really wanted to have local fracking control he could run for a special state office.)

So we can then plausibly conclude that Polis has likely been playing us all, or at least only exploited the initiative drive to get more press for himself.. Sadly, with the initiatives pulled, it means all those 100,000+ who've signed them will likely not be tricked into doing so again  - for another sham cover by a lying politico only seeking to protect his own hide. Meanwhile, the Neoliberal Dem Governor Hickenlooper has again resorted to his usual codswallop, once describing  the push for the local control initiatives and the action by five municipalities to place bans on moratoriums for drilling as "a rebellion". Obviously showing he has no clue what a REAL one looks like, making me wish I could transport him back in time to Yorktown  or Lexington in 1777, oh,  in a Redcoat uniform.

And in his most recent Post remarks:

"There are still a bunch of critics who say we're kicking the can down the road. But if those critics had their way we would be in the middle of a ballot war right now. "

You have that one right, sonny.  And we'd have had a full throated expression of the people's will which you and your imps have now prevented by a back room deal.

Some things never change, but the people of Colorado won't forget. You can make book on it!

Preventing Another Ferguson Incident: The Body Camera!

Photo: Using miniature digital camera - an excellent idea for police!
A Denver Police officer tries out the miniature camera.

Could the upheaval and violence in Ferguson, MO all have been prevented or at least minimized? These are questions now being asked, and very often the response is 'Yes, it could!'  To understand why we note the observation in a recent TIME article ('The Tragedy of Ferguson', Sept. 1, p. 22) that:

"the heart of it all lay two or three minutes just after noon on Saturday, August 9, a fatal span that brought Brown and Wilson together on a stretch of Canfield Drive."

Meaning that within this time interval assorted people reported their separate observations of what transpired and the officer his own. Alas, no settled accounts of the time sequence or actual events exist. This could all have evidently been avoided. How?

Via the use of special miniaturized digital body cameras worn on the side frames of officers' glasses or sun glasses. The tiny cameras record every last detail in any encounter with the public for any reason, and hence provide a firm and accurate document of the officer's actions and the perp's responses or crimes. Basically, it is insurance to protect police from false allegations of excessive force, and also suspects from overly aggressive police actions. The body camera ensures literal, visible accountability. According to Denver Police Chief Robert White :

"The body camera will clear up those moments of conflict"

This was revealed in an NBC News spot last night which focused on the police force in Laurel, Maryland,  where officers have been authorized to use these cameras as a standard operating procedure for the past 18 months.  The result? Crime has dropped 46 percent and the police force has seen accountability for all arrests enhanced by virtue of everything being on record. (In a few cases, as noted in the Denver Post, p. 5A), "people making allegations against the police have withdrawn complaints when they learned their encounters were recorded.")

One instance shown in the Laurel, MD segment involved an officer stopping a speeding vehicle. The entire transaction was recorded including when the officer asked to see identification and the perp floored her accelerator and left the scene - soon later apprehended down the highway.

The benefits from this digital camera system are self-evident. It's no longer a case of the officer's word against anyone else's because he can always provide the evidence in the form of the digital recording. Did he really fire six times into a suspect's body? The camera won't lie and will record all the action from his perspective. If he fired, that will be shown, as well as any reactions by the suspect.

Thus, had Ferguson police officer Darren Wilson been outfitted with such a miniature camera - like the police in Laurel, MD - it is doubtful things would have gotten to the stage they did in Ferguson.  All the events would have been immediately accessible and there'd have been no "fatal span" of time within which witness accounts conflicted.

Clearly, these devices need to be dispensed throughout the U.S. to all police departments,  and I would say as a vastly higher priority than dispensing militarized gear like Humvees.