Sunday, April 27, 2014

Measure for the Path Integral

Quick Reminder to self:

The measure for the path integral, normally written

\begin{eqnarray}
\langle q_F \vert e^{-iHT}\vert q_i \rangle &=& \int Dq e^{\frac{i}{\hbar}\int L(q,\dot{q},t)dt}
\end{eqnarray}

is

\begin{eqnarray}
\int Dq &=& \lim_{N \to \infty}\left( \frac{2\pi m}{i \delta t} \right)^{N/2} \int \cdots \int dq_1 dq_2 \cdots dq_N
\end{eqnarray}

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