Consider the solution to the Schrödinger equation

(1)

where is h-bar, m is the mass of a particle, is the wavefunction, and E is the energy of a given state, for a half-infinite potential, for an infinite one-dimensional square potential well, the potential is given by

(2)

so Schrödinger equation becomes

(3)

for , where

(4)

Fermi Energy, Finite Square Potential Well, Half-Infinite Square Potential Well, Potential Step, Schrödinger Equation, Spherical Potential Well