On the exactness of the Semi-Classical Approximation for Non-Relativistic One Dimensional Propagators

Details On the exactness of the Semi-Classical Approximation for Non-Relativistic One Dimensional Propagators On the exactness of the Semi-Classical Approximation for Non-Relativistic One Dimensional Propagators

2006-08-28

arxiv.org/abs/quant-ph/0608211v2

journal of physics A: Math. Gen. Vol:39 p.14681, 2006

Physics

Quantum Physics

7 pages, latex, no figures, published in journal of physics A

Scientific paper

10.1088/0305-4470/39/47/011

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.

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