Direct Evaluation of Path Integrals

  • Walter Dittrich
  • Martin Reuter

Abstract

Until now we have always used a trick to calculate the path integral in
$$ \begin{array}{l} K({x_2},\;{t_2};\;{x_1},\;{t_1})\;{\rm{ = }}\;{{\rm{e}}^{(i/\hbar )}}{S_{cl}}[x(t)]\;\;\;\int_{y(t1) = 0}^{y(t2) = 0} {[dy(t)]} \\ \;{\rm{ x exp }}\left\{ {\left. {\frac{i}{\hbar }\;\int_{t1}^{t2} {dt} (a(t){y^2}\; + \;b(t)y\dot y\; + \;c(t){{\dot y}^2})} \right\}} \right.\;\;{\rm{.}} \end{array} $$
(17.1)

Keywords

Sine 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Walter Dittrich
    • 1
  • Martin Reuter
    • 2
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenFed. Rep. of Germany
  2. 2.Institut für Theoretische PhysikUniversität HannoverHannover 1Fed. Rep. of Germany

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