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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Functional integral (semiclassic formula)

**Physics Forums | Science Articles, Homework Help, Discussion**