Return to Q&A main page: Q_A
Q&A for the previous lecture: Q_A_1204
Q&A for the next lecture: Q_A_1209

If you want to see lecture notes, click lec_notes

Main class wiki page: home

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?

I don't think the shapes are due to coulomb repulsion, since those wavefunctions were derived for a one-electron atom, like hydrogen. They are simply a result of the math. The difference between the s, p, d, f, etc. orbitals lies in the angular momentum quantum number, l. Since the spherical harmonics <math>Y_{l}^{m}</math> are dependent on <math>\theta</math> and <math>\phi</math> for l not equal to zero, those harmonics are not spherically symmetric.

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.

If Yuichi is taking opinions, I'd prefer we just get an equation sheet instead of making our own. I don't think we even needed one for the last quiz, and I know most equations we need are given to us in the problems anyway. It's a decent way to study having to make our own, but I'd prefer just getting a generic one.

Strangely, I think I'm happy there aren't equation sheets allowed on this quiz. This material seems to be mostly about being able to manipulate what you are given, not about hunting down equations.

I have a general question, so we are not going to go through chapter 5 but there are hw problems from that chapter. and i understand that it is my responsibility to read and learn the material, but is the final going to cover chapter 5 or not. I know the professor said the last midterm will not cover this chapter, but what about the final?

Is problem 5 on the Prac Quiz equivalent to page 174 and 175 with L instead of S? Are they identical b/c l = 1/2 ?

Can somebody explain exactly what we're doing with “corrections” in perturbation theory? I think it means that we're approximating the effect of a perturbation by adding a first or second order approximation of the perturbation to the original wave function, and that an exact solution would require corrections with powers through infinity, but we can argue that higher order corrections become less significant and we'll arrive with a close approximation with just the first one or two corrections. Is this right? Or is there something more that I'm missing?

That is pretty much what I figured since as we go out to further corrections of higher powers they become less significant, therefore we only need to go out at least to the second order to get a fairly accurate energy. When you get right down to it, all this theory really does is take into account that these energy well are not perfect and disruptions can occur within the system.

Return to Q&A main page: Q_A
Q&A for the previous lecture: Q_A_1204
Q&A for the next lecture: Q_A_1209