I am reading "Quantum Mechanics and Path Integrals" (by Feynman and Hibbs) and working out some of the problems... as a hobby of sorts.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Brownian Motion and Path Integrals

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**