Letter to the Editor

Time operator for a quantum singular oscillator

Mladen Martinis ; Division of Theoretical Physics, Ruđer Bošković Institute, 10002 Zagreb, Croatia
Vesna Mikuta ; Division of Theoretical Physics, Ruđer Bošković Institute, 10002 Zagreb, Croatia

Abstract

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 ω 2x 2 + 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.

Keywords

self-adjoint time operator; K3 of the SU(1; 1) group; time-of-arrival operator; SU(1; 1) group generators

Hrčak ID:

305231

URI

https://hrcak.srce.hr/305231

Publication date:

2.11.2003.

Article data in other languages: croatian

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