# Shankar's principles of quantum mechanics solutions

Is there anywhere I can get the missing solutions?

I'm just trying to solve the eigenvalue/vector problem for the spin operator in an arbitrary direction.

I keep screwing up the algebra but can't seem to find any explicit examples on how to do the flipping thing. I've tried 4 books!

Thanks!

## Answers and Replies

What is the question, I don't have the book to hand.

Thanks for the quick reply!

It asks you to work out the eigenvectors (I know the eigenvalues are +/- hbar/2) for:

http://itl.chem.ufl.edu/4412_u97/angular_mom/img245.gif [Broken]

I know what the eigenvectors are, I am just not sure how to get them. I hope it's just some trigonometric identity I've forgotten.

Last edited by a moderator:
Isn't this a one liner?
eigenvector is (a,b)
eigenvalue equation for +1 gives
a cos(t) + b sin(t) exp(-ip) = a
a sin(t) exp(-ip) - b cos(t) = b

rearrange the first equation to get: a = b*[sin(t) exp(-ip)]/[1+cos(t)]
that gives the ratio of the components for the eigenvector for +1.

you can faff about normalising them if you feel like it.
I'm prob missing out the bit you're stuck on?

Can anyone help me by solving this problem form
R Sankar-------Principles of quantum mechanics.

delta(f(x)) = Sum {delta(x-xi)/ abs(df/dx')} ; where xi is the roots of fx .

Does anyone have solution of R Sankar Book for
" Principles of quantum mechanics"

strangerep
Science Advisor
Can anyone help me by solving this problem [...]
$$\delta(f(x)) = \sum_\xi \frac{\delta(x-\xi)}{|f'(x)|}$$
where $\xi$ are the roots of f(x) .

I doubt anyone here will "solve" it for you. But if you invest some effort,
we might help you figure it out.

For starters, write down the definition of the delta fn.

Then, to get the idea, try to prove this simpler formula first:
$$\delta(\alpha x) ~=~ \frac{\delta(x)}{|\alpha|}$$
(Oh, and try to write your formulas here in latex. No one wants to read messy unformatted math. I re-edited your original post to show you how to get started with latex on PF.)

I worked through every problem in that Shankar book, which I thought was a wonderful book.

I found solutions to a large majority of the problems simply by googling "shankar quantum mechanics homework solutions", or similar things along those lines.

It is a bit frustrating looking through the links finding you need passwords for some, others have links that are now old/broken, or etc., but with a bit of searching I bet you could fill in at least some of the problems.

I should probably add that the types of pages you are looking for is the web site for a quantum mechanics class where the teacher posts the homework solutions.