A particle with mass m and energy E is moving in one dimension from left to right. It is incident on the step potential V(x) = 0 for x < 0 and V(x) = V0 for x >= 0, where V0 > 0. The energy of the particle is exactly equal to V0, ie. E = V0.
Solve the Schrodinger equation to derive the wave function for x < 0 and x >= 0. Express the solution in terms of a single unknown constant.