If two (or more) distinct solutions to the (time-independent) Schrdinger equation have the same energy E, these

If two (or more) distinct solutions to the (time-independent) Schrödinger equation have the same energy E, these states are said to be degenerate. For example, the free particle states are doubly degenerate—one solution representing motion to the right, and the other motion to the left. But we have never encountered normalizable degenerate solutions, and this is no accident. Prove the following theorem: In one dimension (-∞< x < ∞) there are no degenerate bound states.