Fernández Guasti, M.; Gil-Villegas, A. Orthogonal functions invariant for the time-dependent harmonic oscillator. (English) Zbl 0988.81030 Phys. Lett., A 292, No. 4-5, 243-245 (2002). 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. Cited in 2 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:Lewis invariant; polar complex solution representation; linear independent solutions PDF BibTeX XML Cite \textit{M. Fernández Guasti} and \textit{A. Gil-Villegas}, Phys. Lett., A 292, No. 4--5, 243--245 (2002; Zbl 0988.81030) Full Text: DOI References: [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, 1, 3 (1978) [4] Fernández Guasti, M.; Diamant, R.; Gil Villegas, A., Rev. Mex. Fı́s., 46, 6, 530 (2000) [5] Landau, L. D.; Lifshitz, E. M., Mechanics (1976), Pergamon Press: Pergamon Press Oxford, pp. 154-157 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.