[UPSC CSE 2014] Schrodinger’s Wave equation and applications (Q179, 20M)

Solve the Schrödinger equation for a particle of mass m confined in one dimensional potential well of the form: V(x)= \begin{cases} 0; & 0 \leq x \leq L,\\ \infty; & x<0,\ x>L. \end{cases} Obtain the discrete energy values and the normalized eigen functions.