Solve Schrodinger’s Equation In Both Spatial And Temporal Part

Question

We consider a potential step where V = U > 0 for x < 0 and V = 0 for x > 0. A particle of energy 0 < E < U is incident from the right of the potential step.

a) Solve the Schrodinger equation everywhere for both the spatial and temporal part. You should express your answer in terms of complete ψ (x; t) in both regions. You do not have to solve for the coefficients or amplitude of the wave function here. You should have only 3 unknown coefficients A; B; C, explain their physical signification.

b) Applying boundary conditions at x = 0, compute the ratio B/A and C/A, with A defined as the coefficient for the incident wave function.

c) Calculate the coefficient of reflexion R. How do you interpret this result? Is there penetration of the wave function in the region x < 0? Is there a propagating wave in this region?

Summary

The question belongs to Physics and it is discusses about solving Schrodinger’s equation in both spatial and temporal part and calculation of coefficient for incident wave function.

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