To illustrate the abstract reduction to dimensionless quantities apply it to the harmonic oscillator V(x) = (m \omega^2 x^2) / 2 using x_0 = sqrt(h-bar/(m \omega)) and find a dimensionless Schrodinger equation. Translate the known solutions to the Schrodinger equation for the harmonic oscillator E_n = (n + 1/2)h-bar\omega into the allowed energies ~E of the dimensionless Schrodinger equation. I know this has to do with dimensional analysis, but I was sick when we had that class, and I've been searching for help on the internet the whole day without any luck. I don't think it is too difficult, I just don't really get what I have to do. I guess the \omega and the m have to go, but how?