# Beyond WKB

1. Apr 27, 2007

### tpm

If in 1-D the WKB wave and energy quantization are:

$$\Psi (x) = e^{iS(x)/\hbar}$$ and $$\oint_C dq p =2\pi (n+1/2) \hbar$$

My question is what happens with more than one dimension ?? (many body system or 3-D system), what happens with QFT ?? i know that as an analogy you could always put the WKB wavefunction in the form:

$$\Psi [\phi] = e^{iS[\phi]/\hbar}$$

but what happens with the energies??..i know this must/can be used when delaing Semiclassical Quantum Gravity won't it ??