[UPSC CSE 2013] Schrodinger’s Wave equation and applications (Q184, 30M)

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(i) Consider a beam of particles incident on a one-dimensional step function potential with energy E > V_0 as shown in the above figure. Solve the Schrödinger equation and obtain expressions for the reflection and transmission coefficients.

(ii) What are the limits of the reflection coefficient for E \to V_0 and E \to \infty?

(iii) Discuss the cases 0 < E < V_0 and E < 0.