Example Question: an electron with mass m is confined in a thin wire, with periodic boundary conditions applied in the x direction and harmonic potentials in the y and z direction. Write an expression for the wave functions in the ground state. Write down all the energy eigen values.
The Attempt at a Solution
I have no trouble deriving the wave function for the periodic boundary conditions.
1. I've used the same method to derive the harmonic potential wave functions as a simple harmonic oscillator, are they the same?
2. I'm having real trouble with knowing the hamiltonian to use for periodic boundary conditions. I (now) understand that the only thing that changes in the hamiltonian for a system is the potential term (and time depencancy). However what would the potential term be for a periodic boundary condition system?
This is a revision question for exams (not assessed).
Thanks in advance for any guidance on this.