Hermite Differential Equation
One encounters this ordinary second order differential equation in solving the one dimensional time independent Schrödinger equation
for a harmonic oscillator. In this case the potential energy V(x) is:
This leads to the following ordinary second order differential equation:
This differential equation has an irregular singularity at ∞. Its solutions are Hermite polynomials.
Read more about this topic: Regular Singular Point
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