hi(adsbygoogle = window.adsbygoogle || []).push({});

i need the schrödinger equation for a particle(electron) in a ring under the influence of a magnetic field that goes through perpendicular to the plane of the ring and i want to consider the spin too.

Well, the particle in the ring is pretty easy:

[itex]- \frac{ \hbar^2}{2mr^2} \psi''(\phi)=E \psi (\phi) [/itex]

but what is about the magnetic field?

i thought that if i take

[itex]E_{pot}=\mu B=\frac{e m v r}{2m}B=\frac{e l B}{2m} [/itex]

and therefore:

[itex]- \frac{ \hbar^2}{2mr^2} \psi''(\phi)+\frac{i \hbar e}{2m} \psi '(\phi) B=E \psi (\phi) [/itex]

and then i would get an additional term if i want to consider the spin:

[itex]E_{pot}=\mu B=\frac{-g_s \mu_B \sigma }{\hbar }B [/itex]

and therefore:

[itex]- \frac{ \hbar^2}{2mr^2} \psi''(\phi)+\frac{i \hbar e}{2m} \psi '(\phi) B+\frac{-g_s \mu_B \sigma }{\hbar }B\psi(\phi)=E \psi (\phi) [/itex]

so, is this the right equation?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Schrödinger equation for particle on a ring in a magnetic field

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**