Abstract
We now want to compute the kernel K(b, a) for a few simple Lagrangians. We have already found for the one-dimensional case that
with
First we consider a free particle,
and represent an arbitrary path in the form,
Here, \(\bar{x}(t)\) is the actual classical path, i.e., solution to the Euler–Lagrange equation:
For the deviation from the classical path, y(t), it holds that
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Dittrich, W., Reuter, M. (2016). Examples for Calculating Path Integrals. In: Classical and Quantum Dynamics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-21677-5_19
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DOI: https://doi.org/10.1007/978-3-319-21677-5_19
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21676-8
Online ISBN: 978-3-319-21677-5
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