- #1

omiros

- 30

- 0

## 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 V

_{0}at x = 0 so that the potential experienced by the particle is;

V(x) = 0 for x < 0 and V(x) = V

_{0}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 V

_{0}. This case corresponds to the solution for an ‘unbound’ particle (E > V

_{0}). Write your wave functions using complex notation; let the amplitudes of the incident, reflected and transmitted waves be C

_{I}, C

_{R}and

C

_{T}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) = C

_{I}*e

^{ikx}+ C

_{R}*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 V

_{0}and at the same time I have to find C

_{T}when the wave has not been exactly transmitted so the equation can't just be C

_{T}*e

^{ikx}(in my point of view)