Universal Journal of Physics and Application Vol. 2(1-2), pp. 69 - 80
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EXISTENCE OF TIME OPERATOR FOR A SINGULAR HARMONIC OSCILLATOR

AUTHOR(S) INFORMATION: Mikuta-Martinis V. and Martinis M.

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.