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## Homework Statement

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.

## Homework Equations

Schrodinger Equation

aΨ

_{0}=0

## The Attempt at a Solution

I have no trouble deriving the wave function for the periodic boundary conditions.

Question:

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.