Potential well — UPSC IFoS 2015 Physics PYQ

Solve the Schrödinger equation for an electron of mass m confined in a one-dimensional potential well of the form

\begin{align*} V &= 0 \text{ when } 0 \le x \le L \\ &= \infty \text{ when } x < 0; \ x > L \end{align*}

Obtain the discrete energy levels and the normalized eigen functions.