Hi. I'm using Maple 16 to model a quantum harmonic oscillator. If I leave the constants k, mu, hbar unspecified, I get a correct solution to the Schrodinger equation:
I would simplify that to 1/2, I tried to force Maple to simplify it for me by setting the three constants all positive, but then I appear to get an inconsistent solution, with an extra factor of sqrt(k):
1. Can you tell me what I'm misunderstanding? If I display the result in the second example, before "simplify", I get all the factors of k to cancel and would get the right answer. Where does the remaining sqrt(k) come from?
2. Can you recommend a way to get the simplification to work (so that I would get "1/2" for the final solution in this example) regardless of the numerical values of k and mu (both positive real)? It would help because my goal is to apply this model to a more complex system, and get the eigenvalues in units of omega using this form. But I can't trust myself to keep the constants straight the way I'm doing it...