###

Energy States of Electrons in a Plasma II

We are going to solve the same plasma in a constant B field in a different gauge.
If
, then

This
gives us the **same B field**.
We can then compute H for a constant B field in the z direction.

With this version of the same problem, we have

We can treat
and
as constants of the motion and solve the problem in
**Cartesian coordinates!**The terms in
and
are actually a perfect square.

This is the **same as the 1D harmonic oscillator equation**
with
and
.

So we get the **same energies with a much simpler calculation**.
The resulting **states are somewhat strange**
and are not analogous to the classical solutions.
(Note that an electron could be circulating about any field line so there are many possible states,
just in case you are worrying about the choice of
and
and counting states.)

Jim Branson
2013-04-22