UVa Physics Review: You know nothing

Sunday, June 27, 2010

You know nothing

It is common for physics grad students to remember the angular momentum operator This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

. Many will even remember that it commutes with This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

and we can therefore form a set of simultaneous eigenfunctions to describe a particle in angular momentum space. Some may even recall that the standard conventions yield the following eigenequations.

But do you know how to demonstrate that This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

and

are the eigenvalues for This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

and

for Stache: This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

2 comments:

James MaxwellJune 27, 2010 at 3:54 PM
I must know nothing. I thought that m was the eigenvalue of Lz by definition. But in my memory, the eigenvalue of L squared follows from the commutation relations. Right?
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lpaJune 30, 2010 at 8:39 AM
You can of course always renormalize the quantum numbers to make one of them whatever you wish. However you still must show that m ranges from -j to j and moves in integer steps. Of course you begin with J_z|j,m> = \mu |j,m> and J^2|j,m>=\lambda|j,m>. Then later you relate \lambda to \mu and then decide to take \mu = m which in turn forces \lambda = j(j+1)
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Keep it to Physics, please.