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WKB approach and energies

  1. Oct 8, 2006 #1
    If we have a 1-dimensional problem so for big n "Energies" can be found in the form:

    [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] ?..:confused: :confused:
  2. jcsd
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