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Time Operator for a Quantum Singular Oscillator

M. Martinis·V. Mikuta
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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 $K_3$ of the SU(1,1) group, the time operator for the quantum singular harmonic potential of the form $ω^2x2 + g/x2$ 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.

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M. Martinis, V. Mikuta. 2002-11-26. Time Operator for a Quantum Singular Oscillator. https://arxiv.org/abs/quant-ph/0211118

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