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Title: On the derivation of the semiclassical approximation to the quantum propagator

In order to rigorously derive the amplitude factor of the semiclassical approximation to the quantum propagator, we extend an existing method originally devised to evaluate Gaussian path-integral expressions. Using a result which relates the determinant of symmetric block-tridiagonal matrices to the determinants of their blocks, two difference equations are obtained. The first one allows to establish the connection of the amplitude factor to Jacobi’s accessory equations in the continuous-time limit, while the second one leads to an additional factor which, however, contributes to the final result only in exceptional cases. In order to demonstrate the wide applicability of these difference equations, we treat explicitly the case where the time-sliced Lagrangian is written in generalized coordinates, for which a general derivation has so far been unavailable.
Authors:
;  [1]
  1. Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg (Germany)
Publication Date:
OSTI Identifier:
22479698
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; COORDINATES; EQUATIONS; LAGRANGIAN FUNCTION; MATRICES; PATH INTEGRALS; PROPAGATOR; SEMICLASSICAL APPROXIMATION; SYMMETRY