Karlisbad
Oct8-06, 01:20 PM
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 ?..:confused: :confused:
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 ?..:confused: :confused: