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From the practice test:

“b. What is the magnitude squared of the total angular momentum (sum of L and S)?”

This is referring to J^2, not simply J, correct?

Correct.

What's the difference between j, J, and <math>\vec{J}</math> ?

(By convention, nothing deeper), <math>\vec{J}</math> refers to an operator for an angular momentum, which is the sum of a few angular momenta. “J” is used when Yuichi is too lazy to write <math>\vec{J}</math> “j” is the quantum number associated with them. i.e. the eigenvalues of <math>\vec{J}^2</math> is <math>j(j+1)\hbar^2</math>. <math>J^2</math> and <math>\vec{J}^2</math> are the same.

I was looking back through the book and was thinking about the shapes of the probability densities of electrons in various wavefunctions (page 157). I can see that these each have unique shapes, but what causes them to be forced into these particular shapes in the first place?

I believe the gnarly shapes are due to couluuuouuuuooooooumb repulsion betwixt thine olde electrinos.

8-)Esquire8-)

Are you guys doing a standing comedy these days?

In any case, I would not say the shapes are due to Coulomb because even for 3D finite square well has the same theta-phi dependence of probability density distribution.

Oh okay, so those shapes are just a result of the probability density functions that we developed in that section?

But that doesn't explain why they are that way-that just says they follow the math we developed. What is the physical significance to each particular odd shape. Like why is the S orbital spherical and the p orbital dumbell shaped?

For the practice test, question 1, am I correct in solving the normalization constant to be theta? This doesn't seem right to me… is there an unwritten constant out front that we're solving for?

I also had this question. I think we are supposed to treat theta as the variable of integration when normalizing. Nom nom nom.

http://www.youtube.com/watch?v=1ZeciX-3wfs

Esquire

Actually one should use equation 4.150 (or a more generalized form of it) for normalizing spin functions.

eq 4.150 |a|^2+|b|^2=1 where a and b are the constants in front of the two spin functions.

Loves and kisses

Esquire

So for the probability of getting would simply be whatever the coefficient in front of chi+ is correct? essentially just the |a|^2 is the probability of 1/2hbar.

Much love,

Chicken

Does this test come with an equation sheet? Are we doing the same thing as before – turning it in on wednesday or something?

Maybe it's to difficult to do in one night-but if at all possible could we turn our sheets in wednesday like for the second test? I hate getting to wednesday night and thursday and changing my mind about what i should have put on there.

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