Hi all,
How to derive the energy of a parabolic confining potential in a wire as shown below? I tried to follow the derivation of the harmonic, oscillator like we did for the quantum well and the magnetic field but i cant find anything that has an expression that come close to the one shown below.
where
I really have no idea how to start and i really appreciate if anybody is willing to guide me or help me. Thanks...
How to derive the energy of a parabolic confining potential in a wire as shown below? I tried to follow the derivation of the harmonic, oscillator like we did for the quantum well and the magnetic field but i cant find anything that has an expression that come close to the one shown below.
I really have no idea how to start and i really appreciate if anybody is willing to guide me or help me. Thanks...
Attachments

1.1 KB Views: 42