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arXiv:quant-ph/9707022

Propagator for a time-dependent harmonic oscillator

John T. Whelan

Published Jul 9, 1997• 0 citations
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Abstract

This paper has been withdrawn, as the explicit form of the propagator can be found in: V.V.Dodonov, I.A.Malkin and V.I.Man'ko, J.Phys.A 8 (1975) L19 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Int.J.Theor.Phys. 14 (1975) 37, Sec.3 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Theor.Math.Phys. 24 (1975) 746, Sec.2 I am grateful to Professor Victor Dodonov for bringing this to my attention.

DOI
10.48550/arxiv.quant-ph/9707022

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This paper has been withdrawn, as the explicit form of the propagator can be found in: V.V.Dodonov, I.A.Malkin and V.I.Man'ko, J.Phys.A 8 (1975) L19 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Int.J.Theor.Phys. 14 (1975) 37, Sec.3 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Theor.Math.Phys. 24 (1975) 746, Sec.2 I am grateful to Professor Victor Dodonov for bringing this to my attention.
We revise the Lewis–Riesenfeld invariant method for solving the quantum time-dependent harmonic oscillator in light of the quantum Arnold transformation previously introduced and its recent generalization to the quantum Arnold–Ermakov–Pinney transformation. We prove that both methods are equivalent and show the advantages of the quantum Arnold–Ermakov–Pinney transformation over the Lewis–Riesenfeld invariant method. We show that, in the quantum time-dependent and damped harmonic oscillator, the invariant proposed by Dodonov and Man’ko is more suitable, and provide some examples to illustrate it, focusing on the damped case.