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

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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.