I know how to do SHO propagator by computing the action. I was only trying to do it(adsbygoogle = window.adsbygoogle || []).push({});

via the eigenfunction expansion

K(x’,x;t)=sum_ i phi_i(x’) phi_i(x) exp(-iε_it/hbar )=(m omega/pi*hbar)

sum_i=-^infty h_i(y’) h_i(y) exp[-(y**2+y’**2)/2] [s(t)/2]**i

with s(t)=exp(-iomega t)

This looks close, but not quite there:

I can get the 1/i! from the Hermite polynomials h_i, and I can use the generating function, but that only applies to a single h, not a product. Am I missing something along this way? I also tried substituting the expression involving (y-d/dy)**i for the h_i, but cannot get it to work

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# SHO propagator

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