The action of the displaced momentum operator on the new eigenstates
is
so the Hamiltonian gives
and the eigenvalues are simply
5.39 Ramp in Square Well (Colorado)
a) For a particle bound in a square well that runs from
the eigenfunction and eigenvalue for the lowest energy state are
The eigenfunction is symmetric and vanishes at the walls of the well.
b) We use first-order perturbation theory to calculate the change in energy
from the perturbation:
288 SOLUTIONS