[UPSC IFoS 2017] Schrodinger’s Wave equation and applications (Q168, 15M)

{ifos-q-5-049-fig-1} A beam of particles of mass m and energy E is incident on a step potential of height V_0 from the left as shown in the figure. Discuss the behaviour of the particle for (i) E < V_0 and (ii) E > V_0. Obtain expressions for the reflection and the transmission coefficients and sketch them as a function of the incident energy of the particle.