On the Lewis-Riesenfeld (Dodonov-Man'ko) invariant method

2015/03/04 by Guerrero, Julio, López-Ruiz, Francisco F.
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1503.01371

Abstract

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 & Man'ko is more suitable and provide some examples to illustrate it, focusing on the damped case.

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