Hi everyone, I have a rather fundamental question about building oscillator wavefunctions numerically. I'm using Matlab. Since it's 1/√(2(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}n!∏)*exp(-x^{2}/2)*H_{n}(x), the normalization term tends to zero rapidly. So for very large N (N>=152 in Matlab) it is zero to machine precision!! Though asymptotic expansions for H_{n}(x) exist in literature (Abromowitz&Stegun, Polyanin&Manzhirov etc), they never say whether these Hermite polynomials are unit normalized for large N. They don't seem to be, i.e these expressions are just H_{n}(x). Numerically is not unlikely to be able to unit normalize unless one takes a extremely large & dense grid. But it is ok for my calculations if these functions have a ||ψ_{N}||^{2}<1, only if they are exactly zero, they drive certain matrices to singularity. so how do people calculate these polynomials without numbers getting exactly zero?? Any help/advice is greatly appreciated!

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# Computing normalized oscillator states for very large N (Matlab)

Can you offer guidance or do you also need help?

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