I have seen discussions which suggests that there is no solution for the interval after the step in a step potential where E = V0. The set up is a potential step where E = V0, with an interval 1 defined as x < 0 before the step and an interval 2 as x > 0 after the step. Is the following correct? Wave equation for interval 1: Ψι = A1eikx + B1e-ikx Wave equation for interval 2: -ħ2/2m d2/dx2Ψ2(x) + v(x)Ψ(x)2 = EΨ(x) v(x)Ψ(x)2 = EΨ(x) So, d2/dx2Ψ(x)2 = 0 In order for d2/dx2Ψ(x)2 to equal 0 d/dx Ψ(x)2 = A2 and Ψ(x)2 = A2x + C So, Ψι = A1eikx + B1e-ikx Ψ2 = A2x Continuity conditions: Ψι = Ψ2 d/dx Ψ1 = d/dx Ψ2 So, A1eikx + B1e-ikx = A2x at interval boundary x = 0 So. A1 + B1 = 0 A1 = B1 i.e. full reflection of the incident wave function. d/dx [A1eikx + B1e-ikx] = d/dx [A2x] ikA1eikx + ikB1e-ikx = A2 at interval boundary x = 0 ikA1 - ikB1 = A2 A1 = B1 So, ik[A1 - A1] = A2 0 = A2 i.e. no transmission of the incident wave function.