8 research outputs found
On the exactness of the Semi-Classical Approximation for Non-Relativistic One Dimensional Propagators
For one dimensional non-relativistic quantum mechanical problems, we
investigate the conditions for all the position dependence of the propagator to
be in its phase, that is, the semi-classical approximation to be exact. For
velocity independent potentials we find that:
(i) the potential must be quadratic in space, but can have arbitrary time
dependence.
(ii) the phase may be made proportional to the classical action, and the
magnitude (``fluctuation factor'') can also be found from the classical
solution.
(iii) for the driven harmonic oscillator the fluctuation factor is
independent of the driving term.Comment: 7 pages, latex, no figures, published in journal of physics