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Orthogonal functions invariant for the time-dependent harmonic oscillator. (English) Zbl 0988.81030
Summary: The Lewis invariant for the time-dependent harmonic oscillator is derived using a polar complex representation of the solution. This derivation is shown to be equivalent to an invariant stemming from the linearly independent solutions. The physical meaning of the involved constants and the associated auxiliary equation are elucidated.

81Q05Closed and approximate solutions to quantum-mechanical equations
Full Text: DOI
[1] Lewis, H. R.: Phys. rev. Lett.. 18, 510 (1967)
[2] Leach, P. G. L.: SIAM J. Appl. math.. 34, 496 (1978)
[3] Lutzky, M.: Phys. lett.. 68A, No. 1, 3 (1978)
[4] Guasti, M. Fernández; Diamant, R.; Villegas, A. Gil: Rev. mex. Fı\acute{}s.. 46, No. 6, 530 (2000)
[5] Landau, L. D.; Lifshitz, E. M.: Mechanics. (1976) · Zbl 0081.22207