Integrals of the motion and green functions for time-dependent mass harmonic oscillators | Zendy

Surarit Pepore | Zendy

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Integrals of the motion and green functions for time-dependent mass harmonic oscillators

Author(s) -

Surarit Pepore

Publication year - 2018

Publication title -

revista mexicana de física

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.181

H-Index - 25

eISSN - 2683-2224

pISSN - 0035-001X

DOI - 10.31349/revmexfis.64.30

Subject(s) - propagator , harmonic oscillator , path integral formulation , eigenfunction , motion (physics) , physics , quantum harmonic oscillator , harmonic , classical mechanics , trajectory , feynman integral , mathematical analysis , connection (principal bundle) , mathematical physics , mathematics , quantum , quantum mechanics , feynman diagram , eigenvalues and eigenvectors , geometry

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.

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