(adsbygoogle = window.adsbygoogle || []).push({}); 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

[itex]\psi[/itex](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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# Homework Help: Schrödinger for a Step

Can you offer guidance or do you also need help?

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