If we have a 1-dimensional problem so for big n "Energies" can be found in the form:(adsbygoogle = window.adsbygoogle || []).push({});

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

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 )

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

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:

[tex] \pi _{ab} [/tex] as the "momenta" conjugate to the metric then the

"Energies" of quantum gravity for big n satisfy

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

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# Homework Help: WKB approach and energies

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