Characteristic decay of the autocorrelation functions prescribed by the Aharonov-Bohm time operator

Details Characteristic decay of the autocorrelation functions prescribed by the Aharonov-Bohm time operator Characteristic decay of the autocorrelation functions prescribed by the Aharonov-Bohm time operator

2001-05-09

arxiv.org/abs/quant-ph/0105033v2

Physics

Quantum Physics

17 pages, REVTeX style file. Some relevant references are added in Sec. 2

Scientific paper

The wave functions, the autocorrelation functions of which decay faster than $t^{-2}$, for both the one-dimensional free particle system and the repulsive-potential system are examined. It is then shown that such wave functions constitute a dense subset of $L^2 ({\bf R}^1)$, under several conditions that are particularly satisfied by the square barrier potential system. It implies that the faster than $t^{-2}$-decay character of the autocorrelation function persists against the perturbation of potential. It is also seen that the denseness of the above subset is guaranteed by that of the domain of the Aharonov-Bohm time operator.

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