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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
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