- #1

crazy-phd

- 8

- 0

during my work on my PhD thesis as an experimental physicist I ended up with a very theoretical problem:

What does the wavefunction of an electron traveling through a magnetic vector potential look like?

I chose a cylindrical coordinate system with a magnetic vector potential A (see eq (1) and (2)) for which I want to solve the Schrödinger equation (3). As there shall be no other potentials present the Hamilton operator looks like equation (4).

Using the considerations for the vector potential my differential equation looks like equation (5). In a first attempt I tried the usual separation of variables (equation (6)) which leads to two differential equations (7) and (8), in which R & Z and R & [itex]\Theta[/itex] are coupled.

Has anybody an idea on how to solve this "beast"?

Thank you