Hi, I am new to QM, so advanced apologies for the dumb questions to follow. What does "the spectrum of boundstates is non-degenerate" mean? And why is the time-independent Schrodinger eqn reflection invariant? (I'm not sure I quite know what that means either...) Thanks!
"Degenerate" energy states are ones which have the same energy. So "the spectrum of bound states is non-degenerate" means no two bound states have the same energy. (This is specific to your system though, and not true in general) A reflection is a transformation of coordinates x -> -x. So it means that the equation gives the same solutions if you invert the coordinate system. (which may also include the _time_ coordinate, since it's time-independent, changing the sign of the time coordinate will by definition not change anything.)