[UPSC CSE 2002] Schrodinger’s Wave equation and applications (Q223, 20M)

Solve the one dimensional Schrodinger wave equation with potential: V(x) = \begin{cases} 0 & \text{for } x < -a \\ V_0 & \text{for } -a < x < a \\ 0 & \text{for } x > 0 \end{cases}