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

Hello! I'm looking at a situation where there is a finite potential Vo for x<0, but zero potential for x>0. For a particle moving from left to right, I'm wondering what coefficients for the solution to the Schrodinger equation are equal to zero, and also how to prove that there is reflection even for a potential drop. hbar is h/(2π).

2. Relevant equations

Time-independent Schrodinger equation

3. The attempt at a solution

Here's what I'm thinking:

For x<0, ψ(x) = 1/√(k0)(Arighteik0x+Alefte-ik0x)

where k0 = √[2m(E+Vo)/hbar2]

For x>0, ψ(x) = 1/√(k1)(Brighteik1x+Blefte-ik1x)

where k1 = √[2m(E)/hbar2]

I think that Bleft is zero, as there is nothing to cause reflection past the potential drop. How can I prove this, and that Aleft is non-zero (ie, potential drop produces reflection)? I know that the wave function and its derivative must be continuous at x=0-- is that sufficient?

Thank you!

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# Schrodinger equation for potential drop

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