engleski

Time operator for a quantum singular oscillator

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 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.

time operator; self - adjoint operator; quantum mechanics

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