classes:2009:fall:phys4101.001:q_a_1207 [School of Physics and Astronomy Wiki]

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
===== Dec 07 (Mon)  =====
**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]]
---------------------------------------
====John Galt 12/6  3:51PM====
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?

===Yuichi===
Correct.

====Daniel Faraday 12/6 430pm====
What's the difference between j, J, and <math>\vec{J}</math> ?

===Yuichi===
(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.

==== joh04684 12/6 1914 ====
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?

=== Esquire 12/6 1914.5 (Age of being in the same room)===

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

//8-)Esquire8-)//

===Yuichi===
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.

=== joh04684 12/7 2033 ===
Oh okay, so those shapes are just a result of the probability density functions that we developed in that section?

===Dark Helmet 12/6 12:39===
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?

=== prest121 12/7 8pm ===
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.

==== Spherical Chicken :  Star date 200912.06 ====
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?  

=== Esquire 12/7 2035 (Age of points) ===

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//

=== Esquire 12/7 2052 (Age of semblance of credibility)===
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//


=== Spherical Chicken ===
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//
==== Spherical Chicken ====
Does this test come with an equation sheet?  Are we doing the same thing as before -- turning it in on wednesday or something?
===Dark Helmet 12/6 21:43===
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.  
===Captain America 12/7 ===
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.
===Hydra 12/7 ===
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.

===Dark Helmet 12/10===
It's not like they helped on the last quiz anyway.  So i bet this quiz will be similar.

====Andromeda 12/6 10/04====
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? 

=== The Doctor 12/8 11:02 PM ===
I would expect there's going to be some amount of chapter 5 on the final.

=== Dark Helmet 12/10===
There is some Chapter 5 on the quiz so i would guess it will be on the final too.
===Devlin  12/20===
Last I heard chapter five is not on the quiz and therefore not on the final as well.  But, that was in lecture last week I believe.

====Green Suit 12/7 1:46====
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 ? 

=== The Doctor 12/8 11:22 PM ===
I haven't actually worked through the practice quiz problem yet, but if it's not the same it's very close.  Once I work through it I'll let you know what I got.

==== Zeno 12/7 5PM ====
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?

===Pluto 4ever 12/7 7:45PM===
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.

==Schrodinger's Dog 12/7==
We look at our ideal cases that we have dealt with in chapter 2. Very nice potentials right? Okay, what happens when we put a hole or a dent in these potentials, obscuring them from their original selves. Well this gives you a really bad problem, right? Well one way to get around this "perturbation" of the potential, is to start with a really pretty nice/easy(well sometime easy), ideal cases. Once we have that, we add the perturbation(i.e. dent) to our potential. Changing our potential certainly changes our wavefunction. Doing this, we can look at other systems that are similar to the ideal easy cases, but which have some weird twist to it(like the system has infinite potential from -a to a and 0 potential for -a to 0 and a potential V from 0 to a). This is similar to our infinite square well, but they are two potentials we have to consider inside the finite region. Using perturbation theory, we can discover the behavior of this system, using the infinite square well, done in chapter 2. Griffths does this example in chapter 6. There is more to this, but this is the basic idea. 

-//7 more days!//-Schrodinger

====Blackbox 12/8====
I can't read the mathematical equations. Could you fix this problem?




---------------------------------------
**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]]**
User Tools

Page Tools
