Abstract
An invariant arising from the linearly independent solutions is evaluated for the time dependent harmonic oscillator equation. The relationship of this quantity with the Lewis invariant is established. The physical meaning of the procedure is stressed. In the adiabatic approximation, the proposed invariant turns into the well known relationship where the energy is proportional to the frequency.
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References
L.D. Landau and E.M. Lifehitz, Mechanics, 3rd ed., (Pergamon Press, Oxford, 1995), p. 154-157.
M.J. Klein, Paul Ehrenfest, 1, (North Holland, Amsterdam, 1972), p. 269.
H.R. Lewis and P.G.L. Leach, J. Math. Phys. 23, 165 (1982).
H.R. Lewis, Phys. Rev. Lett. 18, 510 (1967).
J.R. Ray and J.L. Reid, Phys. Rev. A 26, 1042 (1982).
C.J. Eliezer and A. Gray, SIAM J. Appl. Math. 30, 463 (1976).
G. Arfken, Mathematical methods for physicists, 2rd ed., NY, (Academic Press, 1995) pp. 424-436.
M. Fernández Guasti and A. Gil-Villegas, Phys. Lett. A 292, 243 (2002).
M. Fernandez Guasti, R. Diamant and A. Gil-Villegas, Rev. Mex. Fis. 46, 530 (2000).
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Guasti, M.F., Gil-Villegas, A. (2003). Exact And Adiabatic Invariant For The Time-Dependent Harmonic Oscillators. In: Macias, A., Uribe, F., Diaz, E. (eds) Developments in Mathematical and Experimental Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0199-2_10
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DOI: https://doi.org/10.1007/978-1-4615-0199-2_10
Publisher Name: Springer, Boston, MA
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