[UPSC CSE 2011] Schrodinger’s Wave equation and applications (Q191, 25M)

Solve the Schrödinger equation for a particle of mass m in an infinite rectangular well defined by V(x)=\begin{cases} 0\ ;\ 0\leq x\leq L\\ \infty\ ;\ x<0,\,x>L \end{cases} Obtain the normalized eigen functions and the corresponding eigen values.