[UPSC CSE 2025] Schrodinger’s Wave equation and applications (Q107, 15M)

For a potential with the boundary conditions V(x) = \begin{cases} 0, & x < -a \\\\ V, & -a < x < a \\\\ 0, & x > a \end{cases} solve the Schrödinger's equation in one dimension and find out the conditions for tunnelling.