By simply selecting energies and viewing the wave functions you can begin to understand why some wave functions are acceptable in terms of physics and others are not. For the wave functions on the screen, answer the following questions:
What is the probability of detecting the electron at the edges of the screen, far from the center of the potential?
What should the wave function do at the edges in order to correspond to an allowed energy state?
Is either of these wave function allowable in terms of its physical interpretation? Why or why not?