we know that for the SE equation we find the propagator(adsbygoogle = window.adsbygoogle || []).push({});

[tex] (i\hbar \partial _{t} - \hbar ^{2} \nabla +V(x,y,z) )K(x,x')=\delta (x-x') [/tex]

with m=1/2 for simplicity

then we know that the propagator K(x,x') may be obtained from the evaluation of the Path integral.

[tex] K(x,x')=C \int \mathcal D[x] e^{iS[x]/\hbar} [/tex] (sum over all path X(t) )

my question is, since we can't know the evaluation of the path integral exactly, but give a WKB approach of this if we name the result of the path integral by [tex] K_{WKB}(x,x') [/tex].

then my question is if at least as an approximation this function satisfies.

[tex] (i\hbar \partial _{t} - \hbar ^{2} \nabla +V(x,y,z) )K_{WKB}(x,x')=\delta (x-x') [/tex]

the notation WKB means that we have evaluated the propagator and so on in a semiclassical way.

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# Path integrals and propagators

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