Questions and answers for homeworks in 4410, Sp 98

HW 1

>        I won't be able to make many of your office hours this semester,
>so I am going to have to direct most of my questions to you via e-mail,
>including this one.

 Sorry to hear my office hours are inconvenient for you. If you do need
more than email help, just let me know, and we'll find some time you
can make it! 

>       In problem 2d (Find sum of absolute value of c squared), I have no
>idea how to get started.  I know that the final answer should be one, but
>I don't know how to prove that mathematically.  Is there anything you
>could tell me, just to get started on this problem?

 Maybe looking over Gas' section on the expansion postulate will help
(P.  117,118) . In fact, Gas Eq. 6-23 (or the unnumbered eq'n above it)
is the result you're after, but it's derived in the awkward
"integral"-y way - doing the exact same thing using Dirac notation (see p.
120, 121) might even make it look simple! (It all comes down to the fact
that wave functions are normalized...) 

Hope this helps you get started - 
Steve P. 

HW 7

>Prof. Pollock,
>
>In problem 4 (Gas 16-12 with B field added to hydrogen) can I say that
>the direction of the B field defines the 'z' direction?  Or is that
>going against something that we said when we choose 'm' to be the
>eigenvalue of L_z?  If I can't do the above, is there any other 'trick'
>that keeps me from having to evaluate a 7x7 and a 5x5 matrix?
>
>Thanks.  Sorry about the late notice.


In this problem there is no stated definition of z. So, you get to
choose it!  (The only natural choice is parallel to B, that's fine)

Steve P. 

HW 9

> Prof. Pollock,
>
>        I'm having a real problem with problem Gas. 18-5.  I keep getting
>imaginary numbers for the minimum of the energy corresponding to the
>wavefunction I use.  I have been using Sqrt[a/2Pi]*Exp[-ar].  Could this
>wavefunction be wrong?  Is it possible that Tau = r^2?  Or, perhaps I have
>been using the wrong Hamiltonian.  I have been using p^2/2m + 1/2mw^2r^2,
>however this seems correct to me.
>        Everything else is just calculation.  Plugging it into Mma verfies
>my odd results for the minimum I found by hand.

                                                Thanks,


I'm not sure I agree with your normalization. It looks to me like you
may have forgotten the "r^2" factor in the radial integral? (in 3d =>
use r^2 dr, not just dr)

I think Gas really *does* mean to use Exp[-ar] (if you use r^2 you'll
get the exact answer, but I don't think that's his point here)

Your Hamiltonian is correct. The only other problem I can think of is:
are you using the correct formula for p^2? (Recall, the Laplacian
(del^2) operator is not just d^2/dr^2 in spherical coordinates)

Hope this helps -

HW 11

> Prof. Pollock,
>	I have a real quick question on a couple of the HW questions.
>I'm kind of confused about exactly what Gas. wants us to find in
>problems 13-6,13-8 a.  Does he want us to plug in the functions into
>the equations given and prove that we get out what we are supposed to,
>or does he want us to derive them?



I agree, he's a little ambiguous about this. I think it's fine (and a
lot easier) to just plug in the functions and prove that they satisfy
the equations. (You *could* derive the one in 13-8a, but there's no
need if you don't want to...)

Final

>I was wondering if the previous two exams would be a
>good guide of the type of material which will be on the final exam...



Well, I'd say the previous exams should be a guide to the level and
character of material I like to put on exams... But, the material will
be of course somewhat more focussed on the chapters since Exam #2.
Obvious things to expect would be a TDPT problem, and a Variational
problem and an E+M (Ch. 13) type problem. (since we've spent lots of
time on all three of those!) And, as I mentioned in the last class, I'm
itching to test people on "spectroscopic notation"...   Besides that,
expect one or two questions on older material (where old exams will be
of some use...)

Hope that helps, 

See you Friday, if not earlier,
Steve