# Homework Help: Schrödinger for a Step

1. Mar 14, 2012

### chris_avfc

1. The problem statement, all variables and given/known data

Proton travelling along the x-axis approaches a potential barrier at x = 0

Height of potential barrier - U0 = 20eV
Proton Velocity = 44km/s = 44,000m/s

Asked to show that the solution to the one dimensional time independent Schrödinger equation is
$\psi$(x) = A sin (kx - ϕ)

2. Relevant equations

I know that when the potential is constant and
V(x) = V0 < E

That the solution is the one given, but only because I have read it, I'm not sure how to get get there myself.

3. The attempt at a solution

Reading about it, what I can get is maybe you treat it as one end of an infinite well, so at the step/wall the wave function has to = 0.
Then the need for it to be zero at the walls and non zero away from the wall requires the addition of half a period.
Hence the phi.
But other than that I don't really get it, could anyone help?

Cheers

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