(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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].

2. Relevant equations

Ψ0(x=0) = Ψ1(x=0)

dΨ0(x=0)/dx = Ψ1(x=0)/dx

3. 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

and

ikA' - ikB' = -k1D

How, from this, do I find that

|A'|^2 = |B'|^2

?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Schrodinger's Equation, Potential Energy Barrier U>E

**Physics Forums | Science Articles, Homework Help, Discussion**