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Brownian Motion and Path Integrals

  1. Dec 4, 2011 #1
    I am reading "Quantum Mechanics and Path Integrals" (by Feynman and Hibbs) and working out some of the problems... as a hobby of sorts.

    I have run into a problem in section 12-6 Brownian Motion. On page 339 (of the emended edition), the authors demonstrate, by example, a method for calculating a probability distribution using a path integral.

    The text states that "the integral

    P(D,[itex]\theta[/itex])=[itex]\int exp \left\{ -\frac{1}{2R} \int^{T}_{0} \ddot{x}^{2}\left(t\right) dt \right\} D x\left(t\right) [/itex]

    is gaussian and becomes an extremum for the path

    [itex]\frac{d^{4}\bar{x}}{dt^{4}}[/itex] = 0."

    I am having difficulty recognizing from where this path condition arises. Please let me know if you some insight regarding this problem.
     
  2. jcsd
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