# Eigenfunctions and Energies for Sloped-Bottom Square-Well Potential

Eigenfunctions and Energies for Sloped-Bottom Square-Well Potential

Eigenenergies and eigenfunctions of the potential for and for are obtained numerically. This is treated as a perturbation of the infinite square-well potential, with , for and for . The eigenfunction of the unperturbed problem is denoted by . Note that, for increasing quantum number , the effect of the perturbation diminishes.

E

n

ψ

n

V(x)=s|x-|

x

0

x≤1/2

V(x)=∞

x>1/2

s=0

V(x)=0

x≤1/2

V(x)=∞

x>1/2

th

n

(0)

ψ

n

n