Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Path integral question

  1. Feb 3, 2009 #1

    I'm going through the details of the path integral, and have a question about its derivation.

    When we discretize the time interval and evaluate <p_n|exp(-iH*(t_n-t_n-1)|q_n-1>, a Hamiltonian of the form H(p,q)=T(p)+V(q) becomes a number T(p_n)+V(q_n-1).

    However, when the Hamiltonian contains a term like 1/2*[p*f(q)+f(q)*p], it becomes f(q_n')*p_n with q_n'=(q_n+q_n-1)/2.

    I understand the mathematics behind it but it seems to me that it doesn't really matter whether we use q_n-1 or q_n' as the time interval goes to positive infinitesimal.

    Can anyone explain to me why this actually matters?
    Thanks in advance.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted