Thanks for the reply.
Sorry that's my typo it should be:
##0 \lt r \leq b##
and the second one should be
##r \gt b##
Also in the question it says to suppose there is a deviation from Coulombs law at very small distances (even though there is no evidence for it)
Hi,
I just need someone to check if I am on the right track here
Below is a mutual Coulomb potential energy between the electron and proton in a hydrogen atom which is the perturbed system:
##V(x) =
\begin{cases}
- \frac{e^{2}}{4\pi\epsilon_{0}}\frac{b}{r^{2}} \text{for } 0<r \leq 0 \\
-...
Couldn't resist.
I understand the approach here and it is so much clearer than what I was doing before, the only thing I'm not clear on is the ##\frac{2}{L}## factor you have in the approach above.
When I worked out the spatial wave function at the start I multiplied the ##\frac{\sqrt2}{\sqrt...
Thanks for all your help and advice with this. Its gotten me so much closer to an answer than I would have been.
Time is becoming a bit of an issue as this is due in on Monday and I have one more question to look at. So I'm going to leave this for now and hopefully come back to it over the...
No but the factor I am working with from the probability density is ##\frac{1}{L}## not ##\frac{2}{L}## in which is in post 13. Should I be using ##\frac{2}{L}##?
I've had a bit of time this morning to look at this and I have had another go. Here is my attempt:
##\frac{1}{L}\int_0^\frac{L}{2} sin^{2}(\frac{\pi x_{1}}{L})dx_{1} = \frac{1}{L} (\frac{L}{4}) = \frac{1}{4}##
##\frac{1}{L}\int_0^\frac{L}{2} sin^{2}(\frac{2\pi x_{2}}{L})dx_{2} = \frac{1}{L}...
Thanks for the tip, makes it all a lot clearer and easier to set out.
Thanks for all your help so far. I'm going to have to leave it for now and come back to it tomorrow but I'm happy I'm much closer to a solution now.
Ok, fingers crossed:
For the quadratic expansion I now get (fixing the factor and 2 in front of the second term):
##\frac{1}{L}[sin^{2}(\frac{\pi x_{1}}{L})sin^{2}(\frac{2\pi x_{2}}{L})+2sin(\frac{\pi x_{1}}{L})sin(\frac{\pi x_{2}}{L})sin(\frac{2\pi x_{1}}{L})sin(\frac{2\pi...
Ok if possible it would be great to check over my work here and maybe some advice on how to proceed as I've hit a brick wall with some integration.
In the next part of the question I have two indistignishable particles in an infinite square well with walls at x=0 and x=L.
Firstly, I need to...