Path integral analysis of harmonic oscillators with time-dependent mass

Surarit Pepore

Deepika Janakiraman, Kizhakeyil L. Sebastian

Ping Wang, Yang Xin-E, Song Xiao-Hui +1 more

Using coordinate-transformation we transformed a harmonic oscillator with time-d ependent mass and a time-dependent inverse potential into a harmonic oscillator with time-independent mass and a time-independent inverse potential accordingly. In terms of the relation between these two different harmonic oscillators' prop agators we derived the exact wavefunction of the former by Feynman path-integral . We also discussed the harmonic oscillator with more additional potentials.

Bancha Kirdmanee, Surarit Pepore, Bodinchat Sukbot

We demonstrate that the use of a space-time transformation in path integral can simplify the calculation of the propagator for a harmonic oscillator with time-dependent mass and frequency. We show that such a propagator can be easily obtained from the unit mass and frequency propagator in the new space-time coordinate systems. Two cases of harmonic oscillator with time-dependent mass, which exact propagator can be evaluated, are investigated.

Badri Berrabah, Baya Bentag

We have presented a particular direct method to solve time-dependent quantum problems within the framework of path integrals by using explicitly time-dependent transformations. We have applied it to the case of harmonic oscillator with time-dependent mass and frequency. Some examples have illustrated the method used. From their exact propagators, normalized solutions have been obtained.

Bin Kang Cheng