[UPSC CSE 2010] Schrodinger’s Wave equation and applications (Q194, 30M)

{q-5-026-fig-1} A stream of particles of mass M and energy E is directed from left to a one-dimensional potential barrier as shown in the above figure. Set up the time-independent Schrodinger equation and obtain an expression for transmission probability from region I to II. How this phenomenon helps in the understanding of \alpha-decay of nuclei?