Computing normalized oscillator states for very large N (Matlab)

1. Jun 27, 2014

srihari83

Hi everyone, I have a rather fundamental question about building oscillator wavefunctions numerically. I'm using Matlab. Since it's 1/√(2nn!∏)*exp(-x2/2)*Hn(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 Hn(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 Hn(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 ||ψN||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!

Last edited: Jun 28, 2014