[UPSC CSE 2023] Schrodinger’s Wave equation and applications (Q127, 15M)

Consider a stream of particles of mass m each moving in the positive x-direction with kinetic energy E towards the potential barrier V(x) = 0 \quad \text{for } x \le 0 V(x) = \frac{3E}{4} \quad \text{for } x > 0 Find the fraction of particles reflected at x = 0.