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TISE for unbound particle
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[QUOTE="omiros, post: 4545786, member: 480725"] [h2]Homework Statement [/h2] 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 V[SUB]0[/SUB] at x = 0 so that the potential experienced by the particle is; V(x) = 0 for x < 0 and V(x) = V[SUB]0[/SUB] for x ≥ 0 [h2]Homework Equations[/h2] Determine the time-independent wave function for the particle in the case where the particle energy, E, is greater than V[SUB]0[/SUB]. This case corresponds to the solution for an ‘unbound’ particle (E > V[SUB]0[/SUB]). Write your wave functions using complex notation; let the amplitudes of the incident, reflected and transmitted waves be C[SUB]I[/SUB], C[SUB]R[/SUB] and C[SUB]T[/SUB] respectively. Define the wavenumber, k, in the region x < 0 and the wavenumber k' in the region x ≥ 0 . [h2]The Attempt at a Solution[/h2] ψ(x) = C[SUB]I[/SUB]*e[SUP]ikx[/SUP] + C[SUB]R[/SUB]*e[SUP]-ikx[/SUP] 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 V[SUB]0[/SUB] and at the same time I have to find C[SUB]T[/SUB] when the wave has not been exactly transmitted so the equation can't just be C[SUB]T[/SUB]*e[SUP]ikx[/SUP](in my point of view) [/QUOTE]
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TISE for unbound particle
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