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Comment on “Demystifying the constancy of the Ermakov-Lewis invariant for a time-dependent oscillator”. (English) Zbl 1392.34032

Summary: We show that a simple modification of the Lagrangian proposed by T. Padmanabhan [ibid. 33, No. 7–8, Article ID 1830005, 5 p. (2018; Zbl 1383.34055)] leads to the most general dynamical invariant in [J. R. Ray and J. L. Reid, “More exact invariants for the time-dependent harmonic oscillator”, Phys. Lett. A 71, No. 4, 317–318 (1979; doi:10.1016/0375-9601(79)90064-1)].

MSC:

34C14 Symmetries, invariants of ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
81T99 Quantum field theory; related classical field theories

Citations:

Zbl 1383.34055
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References:

[1] Padmanabhan, T., Mod. Phys. Lett. A, 33, 1830005, (2018) · Zbl 1383.34055
[2] Ray, J. R.; Reid, J. L., Phys. Lett. A, 71, 317, (1979)
[3] Mancas, S. C.; Rosu, H. C., Phys. Lett. A, 378, 2113, (2014)
[4] Ray, J. R.; Reid, J. L., Phys. Lett. A, 26, 1042, (1982)
[5] Leach, P. G. L., J. Math. Phys., 22, 465, (1981)
[6] Cariglia, M.; Galajinsky, A.; Gibbons, G. W.; Horvathy, P. A., Eur. Phys. J. C, 78, 314, (2018)
[7] Gelfand, I. M.; Fomin, S. V.; Silverman, R. A., Calculus of Variations, (1963), Prentice-Hall
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