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Revista brasileira de fisica

Coherent states for certain time-dependent systems

I. A. Pedrosa

Published Jan 1, 1989• 4 citations
OpenAlex

Abstract

Hartley and Ray have constructed and studied coherent states for the time- dependent oscillator. Here we show how to construct coherent states for more general time-dependent systems. We also show that these states are equivalent to tl;e well-known squeezed states.

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Physical consequences of the theorem of equivalence among harmonic oscillators of different frequencies, including a free particle as a special case, are explored. A new pictorial way of understanding time-dependent coherent states and squeezed states are presented and contrasted with the standard view. Three-dimensional spherical analogues of squeezed coherent states are constructed. It is also shown as a corollary of the theorem that a free wave packet which coincides initially with any one of the eigenfunctions of a harmonic oscillator maintains its shape, that is, the probability density of position does not change apart from a time-dependent scaling of spatial coordinates. Most of the results are derived without use of any sophisticated techniques but with the knowledge of free wave packets alone.