How Does a Potential Step Affect Particle Wave Functions and Traveling Waves?

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The discussion centers on a beam of particles encountering a potential step, with a focus on the time-dependent wave function psi(x,t) and its interpretation as traveling waves. Participants express confusion over the necessity of a single time-dependent solution given that solutions vary across different regions of the potential. The distinction between regions where the potential is zero and where it is V0 complicates the understanding of wave behavior. Clarification is sought regarding how to reconcile these differing solutions in the context of traveling waves. The conversation highlights the complexities of quantum mechanics in relation to potential steps and wave function behavior.
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Homework Statement



a beam of particles of energy E and mass m is incident from the left on a potential step of height V0 such that
V(x)=0 x<0
V(x)=V0 x>0

what is the full time dependent solution psi(x,t) and what is its interpretation in terms of traveling waves?

The Attempt at a Solution


why is it talking about the time dependent SOLUTION when the solutionS are different in different regions? as for the traveling waves bit, I have no idea
 
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The solution is the set of solutions in different regions.
 

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