# WKB approach and energies

1. Oct 8, 2006

### Karlisbad

If we have a 1-dimensional problem so for big n "Energies" can be found in the form:

$$2 \int_{a}^{b}dx \sqrt (E_{n} - V(x) ) = (n+1/2) \hbar$$

where "a" and "b" are the turning points, then could we writte the equation for energies (where a>c>b using Mean-value theorem for integrals )

$$2 \sqrt (E_{n} - V(c) )(b-a) = (n+1/2) \hbar$$

for finite a,b,c ?

-Another question, when dealing with Semiclasical Quantum Gravity, do the "Energies" satisfy the same WKB constraint?, in particular if we define:

$$\pi _{ab}$$ as the "momenta" conjugate to the metric then the

"Energies" of quantum gravity for big n satisfy

$$\oint dV\pi _{ab}(x,y,z) = (n+1/2) \hbar$$ ?..

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