Recently I had a quiz in my physics class and I feel like the professor made a mistake on the solution for it. Yes, I already have the answer to this question. I am not trying to get people's answers for homework or anything. But I would like to hear people responses to this. The question was:
Which of the following conditions are necessary restrictions imposed on the solutions of the one dimensional Schrodinger equation? (Choose all the apply)
1. The wave function must be continuous.
2. The wave function needs to be normalized.
3. The wave function must converge to zero as x tends to positive and negative infinity.
4. The wave is zero at the boundary conditions
I know that the first three are correct because they are right out of the book. But my problem lies with the last one. So far we have only dealt with a particle in a rigid box and in the derivation, the wave function was zero at the boundary conditions. That's why I said 4 was correct too. This was before we studied finite potential wells where the wave function exponentially decays at the boundaries. So with knowing our limits to the material for the quiz, do you guys think it is fair that he take points off for saying the wave function zero at the boundary condition when it really is zero at the boundary with what we were studying?