Consider particles incident on a potential energy step with E<U.
(That is, a particle with total energy E travels along one dimension where U=0, then crosses, at point x=0 into a region where U>E.) (The particle is incident on the potential energy step from the negative x direction.)
Starting with the wave functions,
x < 0: Ψ0 = A’e^(ikx) + B’e^(-ikx), k = 2mE/h_bar2
x >= 0: Ψ1 = Ce^(k1x) + De^(-k1x), k1 = 2m(U-E)/h_bar2
Apply the boundary conditions for Ψ and dΨ/dx and show that the full wave intensity is reflected at the step [i.e., |A'|^2 = |B'|^2].
Ψ0(x=0) = Ψ1(x=0)
dΨ0(x=0)/dx = Ψ1(x=0)/dx
The Attempt at a Solution
I set C=0, or else the wave function Ψ1 may become infinity.
The boundary conditions are stated above. They become
A' + B' = D
ikA' - ikB' = -k1D
How, from this, do I find that
|A'|^2 = |B'|^2