The Jacobi principal function in quantum mechanics

RAFAEL FERRARO

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

IOP Publishing Ltd.

Lugar: Bristol; Año: 1999 vol. 32 p. 2589 - 2599

0305-4470

The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points—qk and pk+1 or pk and qk+1—through the invariant complete solution of the Hamilton–Jacobi equation associated with the classical path defined by these extremes. When the measure is chosen to reflect the geometrical character of the propagator (it must behave as a density of weight 1/2 in both of its arguments), the resulting infinitesimal propagator is cast in the form of an expansion in a basis of short-time solutions of the wave equation, associated with the eigenfunctions of the initial momenta canonically conjugated to a set of normal coordinates. The operator ordering induced by this prescription is a combination of a symmetrization rule coming from the phase, and a derivative term coming from the measure.