TISE for unbound particle

  • Thread starter omiros
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  • #1
omiros
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Homework Statement


A particle with mass m moving in the positive x -direction (i.e. from left to right) is incident on a potential step of height V0 at x = 0 so that the potential experienced by the particle is;
V(x) = 0 for x < 0 and V(x) = V0 for x ≥ 0

Homework Equations



Determine the time-independent wave function for the particle in the case where the particle energy, E, is greater than V0. This case corresponds to the solution for an ‘unbound’ particle (E > V0). Write your wave functions using complex notation; let the amplitudes of the incident, reflected and transmitted waves be CI, CR and
CT respectively. Define the wavenumber, k, in the region x < 0 and the wavenumber
k' in the region x ≥ 0 .

The Attempt at a Solution


ψ(x) = CI*eikx + CR*e-ikx for x < 0 (is probably the first part of the equation).

My main problem is what to do with the second one, as the particle is constantly 'under the influence' of the potential V0 and at the same time I have to find CT when the wave has not been exactly transmitted so the equation can't just be CT*eikx(in my point of view)
 

Answers and Replies

  • #2
BruceW
Homework Helper
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you are right for the case x<0. And for the case x>0, yes, the particle is essentially in a constant potential V0. In the region x>0, the particle has been transmitted. True, the equation is not CT*eikx. Try using the Schrodinger equation to find what the wavefunction should look like for x>0.
 

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