FIZIKA B 12 (2003)  4, 285 - 290

LETTER TO THE EDITOR

TIME OPERATOR FOR A QUANTUM SINGULAR OSCILLATOR

MLADEN MARTINIS and VESNA MIKUTA

Division of Theoretical Physics, Ruđer Bošković Institute, 10002 Zagreb, Croatia

Received 24 November 2003;    Accepted 15 December 2003
Online 19 April 2004

The problem of existence of a self-adjoint time operator conjugate to a Hamiltonian with SU(1,1) dynamical symmetry is investigated. In the space spanned by the eigenstates of the generator K₃ of the SU(1,1) group, the time operator for the quantum singular harmonic potential of the form w²x² + g/x² is constructed explicitly, and shown that it is related to the time-of-arrival operator of Aharonov and Bohm. Our construction is fully algebraic, involving only the generators of the SU(1,1) group.

PACS numbers: 03.65.Fd, 02.30.Tb
UDC 530.145

Keywords: self-adjoint time operator, K₃ of the SU(1,1) group, time-of-arrival operator, SU(1,1) group generators

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