# Infinite solenoid with magnetic flux

1. Dec 29, 2004

### yxgao

Hi,
I have a question as follows.

For an infinite solenoid with magnetic flux $$\Phi$$, for what values of $$\Phi$$ "is the quantum mechanical motion of an electron constrained to stray far from the solenoid exactly the same as it would be if $$\Phi$$ were zero"?

Solution:
$$\Phi$$ = $$n \Phi_{o}$$ with n = integer and $$\Phi_{o} = \frac{h c}{e}$$

Can someone please explain the solution? I don't understand the concepts involved here. Thanks.

Last edited: Dec 29, 2004
2. Dec 29, 2004

### dextercioby

It deals with the famous Bohm-Aharonov effect and magnetic fkux quantization in superconductors.The trick is to exploit the fact that the magetic field is gauge invariant and in the Hamiltonian it enters not through the field,but through the magnetic vector potential.

A nice discussion is made here:
http://hep.ucsd.edu/~branson/130/130b/130b_notes_prod/node50.html [Broken]
This is node 50,read node 51 as well.

Daniel.

Last edited by a moderator: May 1, 2017