Finding the mean orbital radius of the proton's wavefunction.

So I think I know how to do part A. Assuming that the given .527 angstroms is the distance from the center of mass to the electron I can find the distance from the center of mass to the proton. My center of mass then comes out to be inside the proton. I think that it the right answer but I am not sure. I have no clue how to do parts B and C though. If someone could do this problem I would be very grateful.

Semi-Infinite Square Well Potential

I need to see how to do these types of problems. I know that on the left side psi of 0 would be 0 since this is an infinite well on this side. The problem makes it sound as if I should put E2 slightly slightly below the 0 line. The function inside the well would be sinosoidal and on the right side a decaying exponential. They would be equal at x=a and their derivatives would have to be equal as well. I think that's how I should approach it unless E2 is supposed to be slightly above the well. So if someone can do this problem step by step I would really appreciate it.

Repulsive Delta Function Potential

This is another type of potential that I do not know how to deal with. It will probably turn out to be easy but I don't know how to start this problem. If someone could work it out for me I would be very grateful.

Finite Square Well

Initially, I thought that this would be an easy problem but it turned out to be a bit more complicated than I thought. We're given k*a and can figure out kn pretty easily. Then we could just set it equal to k for a finite square well which is given in the attached information. However, this is where it started to become confusing. In the information provided k is related to Schrodinger equation outside the well and l is related to SE inside the well. To me it would make more sense to equate the given k in this problem to l given in the book. However, then I would have extra Vo term for my ground state energy. In an infinite square well there was no Vo term so I do not know if this is right ... click for more

Energy eigenvalues of: a) Truncated harmonic oscillator b) Logarithmic potential

See attached file.