Soluble Time-Dependent Systems

Costas John Efthimiou, Donald Spector

We use separation of variables as a tool to identify and to analyze exactly soluble time-dependent quantum-mechanical potentials. By considering the most general possible time-dependent redefinition of the spatial coordinate, as well as general transformations on the wave functions, we show that separation of variables applies and exact solubility occurs only in a very restricted class of time-dependent models. We consider the formal structure underlying our findings, and the relationship between our results and other work on time-dependent potentials. As an application of our methods, we apply our results to the calculation of propagators.

V. M. Akulin

J. Révai

Jacob Nissim Israelachvili

Hiroshi Kuratsuji

We investigate a semiclassical quantization of time-dependent classical field for an exact soluble one-dimensional boson systems. The classical field equation admits the analytic solution of soliton type, by which the semiclassical bound state spectrum is evaluated which reproduces the exact quantum mechanical spectrum in good accuracy.

Charles E. Burkhardt, Jacob J. Leventhal