energy values of a "half" harmonic oscillator This is the full question: Find the solution to the "half" harmonic oscillator: Compare the energy values and wave functions with those of the full harmonic oscillator. Why are some of the full solutions present and some missing in the "half" problem? I'm having some trouble figuring out how to find a solution for the wave function of a "half" harmonic oscillator. I can picture what this would look like, since if we "halved" a harmonic oscillator the left end point for energy levels E_1, E_3, E_5 and so on wouldn't be any good since the left end point would no longer be zero at the boundary. I'm having some trouble figuring out how I should adapt the time-indepedent Schrodinger equation to these new boundaries because the book we use only mentions it briefly in the appendix. I don't even know what equation to look at because when I searched it online I got an equation that looked different from my book.