If to calculate the propagator K(x,x') (vaccuum)for a theory so:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] (i\hbar \frac{\partial}{\partial t}\Psi - H\Psi )K(x,x')=\delta (x-x') [/tex] (1)

we use the functional integral approach:

[tex] K(x,x')=<0|e^{iS[x]/\hbar }|0> [/tex]

my question is, let's suppose we use the semiclassical WKB approach to calculate [tex] K_{WKB} (x,x') [/tex] my question is ¿does the classical propagator satisfies the Schöedinguer equation (1) or as an approximation i'd like to know if the semiclassical propagator satisfies a Hamilton-Jacobi type equation... thanks.

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# Functional integral (semiclassic formula)

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