# Electron in a B field.

1. Mar 25, 2013

### port31

Lets say I have a spin-1/2 particle that is about to enter a non-constant B field.
the spin 1/2 particle has a state vector of
$|\psi>= \frac{|+z>}{\sqrt{2}} + \frac{|-z>}{\sqrt{2}}$
What if the B field was also in a superposition like
$|\psi>= \frac{ \sqrt{2}|+B>}{\sqrt{3}}+\frac{|-B>}{\sqrt{3}}$
where B is some non constant magnetic field.
How would I figure out what is the probability of the B field being up or down?
Would it also depend on how the electron interacts with it.
Maybe we should change our particle to a neutron so the Lorentz force wont dominate.

2. Mar 25, 2013

### Staff: Mentor

It is confusing to use the same state description for spin and B-field. I don't know how to get such a superposition, but you can track the evolution of all 4 components (spin up, magnet up, spin up, magnet down, and same for spin down) individually, and add them afterwards.
Instead of electrons, silver atoms can be used.