I have a problem. I am trying to selfteach myself QM but I got stumped with this. Basically, in the issue of 1D step potentias, I know that you have to divide the problem into regions and solve the schrodinger equation for each one. However, when you solve it, you always get two solutions due to the nature of the second order linear differential equation. (One representig a current oming from the left and the other from the right) However, I know sometimes one of the solutions vanishes. For ezample. if V>E in a<x<infinity, the solution will be an exponential wih negative exponent because the positive one vanishes (due to the physicallity of quantum tunneling. In certain instances there will be two solutions because of reflection, etc. However, how do I know when a solution vanishes? Are they rules of thumb or you simply solve for the coefficients using initial conditions?