Recent content by James_1978

Dear Forum, I have a question about the derivation of the Fermi golden rule in Kenneth Krane's Introduction to Nuclear Physics. I understand everything up to equation 9.20. However, it is unclear how he goes directly to equation 9.21. Here is equation 9.20, ## d\lambda =...

Yes. I actually found out how to do it....I think. If you want I can send it to through email. I was missing something very simple in the textbook. I totally missed this ##\psi(r) = u(r)/r##. This solve many of the problems.

Ok. I think I now have this figured out. But I have a general question. I have been getting stuck on the following. The question goes as follows: ##<T> = \frac{\hbar^{2}}{2m} \int_{0}^{\infty} |\frac{\partial\psi}{\partial r}|^{2} dv## Where ##dv## is ##4\pi r^{2}dr##. However, everything...

Yes. Thank you for spending the time to look at this. I appreaciate your help.

This is what I get without evaluation from 0-R. Clearly, the question is asking you to NOT include the ##4\pi r^{2}##. Do you agree?

From Krane Problem 4.3

My mistake. I forgot the k underneath with has units inverse length. So it holds.

Here is the question from the book. The condition for the existence of a bound state in the square-well potential can be determined through the following steps. a) Using the complete normalized wave function, equation 4.3 and 4.4 from the book, show the expectation value of the potential...

Thank you very much for your help. However, I am still not getting the connection as suggested by you. In post #10 you say It starts from the form that the text applies and ends with Laplacian which you described I am not able to see that. What is more confusing is the first part of this...

you wrote it yesterday.

This one ##-\hbar^2 \frac{1}{r}\frac{\partial^2 }{\partial r^2}r##

I have a question. In post #2 you square the radial momentum operator. Why is the ##1/r## and ##r## not squared?

I see what you are saying now. I will try that. I guess I also got confused when I put the ##r^{2}## after the operator.

Yes, that is right. But the last term in the last equation in post #4 is what we are supposed to use. I am still not connecting that to the Laplacian. Are you saying ##<T> = \int\psi^{*}\frac{1}{r^{2}}\frac{\partial}{\partial r}(r^{2}\frac{\partial}{\partial r})\psi d^{3}\overrightarrow{r}##...

Yes. You are saying that this is the same as what you have in post #4? That is integration by parts. By the way in post #4 your middle term and the last term in the last equation are the same. Is that correct?