Abstract

PEPORE, Surarit. Integrals of the motion and Green functions for time-dependent mass harmonic oscillators. Rev. mex. fis. [online]. 2018, vol.64, n.1, pp.30-35. ISSN 0035-001X.

The application of the integrals of the motion of a quantum system in deriving Green function or propagator is established. The Green function is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phase space. The explicit expressions for the Green functions of the damped harmonic oscillator, the harmonic oscillator with strongly pulsating mass, and the harmonic oscillator with mass growing with time are obtained in co-ordinate representations. The connection between the integrals of the motion method and other method such as Feynman path integral and Schwinger method are also discussed.

Keywords : Integrals of the motion; Green function; Time-dependent mass harmonic oscillators.

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