# Hermite Equation use

## Main Question or Discussion Point

I have a problem for a Math Physics course, that I was suppose to find the Hermite equation, find solutions to it, plug them in to see if they work, and lastly find a use for the Hermite equation. I've done everything but I can't find a use for the equation I looked almost everywhere I would really applicate the help if someone could give me a use for the equation, it would be best if it was used in physics but if not it's alright. THANK YOU for the help!

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Hermite Equation as in the differential equation producing the Hermite polynomials?

For the case of a particle in a harmonic potential ($\frac{1}{2}m\omega^2x^2$) in quantum mechanics, the Schrodinger Equation (once rescaled to be in terms of nondimensional variables) has solutions which are proportional to $\exp[-x^2/2]$ times the Hermite polynomials.

http://en.wikipedia.org/wiki/Hermite_polynomials

I can't find the series solution to this equation can someone post it here please, also I was wondering how it fit in with shrodingers equation I'm suppose to somehow use Hermite to get to Schrodinger, or vice versa?

HallsofIvy