[UPSC CSE 2000] Schrodinger’s Wave equation and applications (Q227, 40M)

A 500\ \mu\text{A} beam of electrons of kinetic energy 1.5\text{ eV} enter a region with a sharply defined boundary in which their energy is reduced to 10\text{eV} by a difference of potential. Determine the reflected and transmitted currents. Derive the formulae used.