Hermite Recursion Rule

Next we should note a useful recurrence relationship between the Hermite polynomials. qHnCq) = rMn-iiO + which relates a given w-level to the levels above and below. 

The wave functions are also orthogonal because the product of an odd and even function integrated over all space is zero and the (even x even) or (odd x odd) products cancel due to the 

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This evolution of a complex set of numbers from something very simple is rather like a recursion rule. For example, the wave function for a harmonic oscillator contains the Hermite polynomial, Hb(t/), which satisfies the recursion relation ... 

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