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Existence of Time Operator for a Singular Harmonic Oscillator

V. Mikuta-Martinis·M. Martinis
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Abstract

The time operator for a quantum singular oscillator of the Calogero-Sutherland type is constructed in terms of the generators of the SU(1,1) group. In the space spanned by the eigenstates of the Hamiltonian, the time operator is not self-adjoint. We show, that the time-energy uncertainty relation can be given the meaning within the Barut-Girardello coherent states defined for the singular oscillator.We have also shown the relationship with the time-of-arrival operator of Aharonov and Bohm.

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V. Mikuta-Martinis, M. Martinis. 2005-03-23. Existence of Time Operator for a Singular Harmonic Oscillator. https://arxiv.org/abs/quant-ph/0503187

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