5
votes
1answer
232 views

Approximate analytic solution of Schroedinger equation with arbitrary power potential

I'm solving the following Schroedinger equation in the domain $r>0$ $\psi''(r) + \left(E-\frac{a}{r^b}\right)\psi(r)=0 $, where $0 < b < 2$ and $a, E$ are positive constants. Primarily I'm ...
7
votes
2answers
368 views

Does there exist a potential which realizes this strange quantum mechanical system?

I have done some courses on quantum mechanics and statistical mechanics in the past. Since I also do math, I wonder about converge issues which are usually not such a problem in physics. One of those ...
1
vote
3answers
1k views

Justification for the matching condition for the wave function at potential jumps. Why is it both restrictive enough and sufficiently general?

Consider Schrödinger's time-independent equation $$ -\frac{\hbar^2}{2m}\nabla^2\psi+V\psi=E\psi. $$ In typical examples, the potential $V(x)$ has discontinuities, called potential jumps. Outside ...