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Is this solvable?

  1. Apr 5, 2006 #1
    I would like to know if the functional integral:

    [tex] D[\phi]e^{iS[\phi]/\hbar [/tex] (1)

    where S is the classical action of a system of a Lagrangian with a potential in the form:

    [tex] V=\sum_{n}\delta(x-n) [/tex] n=0,1,2,3,4,5,6,...........

    The Schroedinguer equation if the sum is finite can be transformed into a solvable "integral equation"..but i would like to know if the functional is exactly integrable,...by the way i would like to know how Feynmann obtained the Schroedinguer equation by calculating the infinite integral (1) for S the action:

    [tex] S=\int_{a}^{b}dt\alpha{(dx/dt)^{2}} [/tex]

    then this integral in (1) would be a Gaussian and could be calculated exactly but how you derive Schroedinguer equation?..thanks.
  2. jcsd
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