PREPARATION OF PAPERS FOR JOURNAL SCIENCES & TECHNOLOGIES A.
الكلمات المفتاحية:
Path integral، Time dependent mass، time dependent harmonic oscillator، time dependent transformationsالملخص
We present a space-time transformation to the harmonic oscillator with a time-dependent mass and frequency and we transform the problem to that of constant mass and time-dependent potential of the form . The propagator and the corresponding wave functions are given. A new general model of time-dependent mass is proposed.
التنزيلات
المراجع
Colegrave RK and Abdalla MS (1981) Harmonic oscillator with exponential decaying mass. J Phys A 14, 2269-80
Berger BK (1975) Scalar particle creation in an anisotropic universe .Rhys Rev D 12, 368-75
Brown LS (1991) Quantum motion in a Paul trap. Phys Rev, lett 66, 527-9
Y.Ben-Aryeh and A.Monn, Phys Rev. lett. 54, 1020 (1985).
R.K.Colegrave and M.S.Abdalla, Opt.Acta 28, 495(1981); R.K. Colegrave and M.S. Abdalla, Opt. Acta 30, 849(1983); R.K.Colegrave and M.S.Abdalla, Opt. Acta 30, 861(1983).
D.C.Khndekar, S.V.Lawand, K.V.Bhagwat, path integral method and their applications (WorldScientific,Singapore, 1990)
M.Sabir, S.Rajagopalan, Path integral of harmonic oscillators with time-dependent mass; J.Phys,Vol.37, 3, (1991)
H.R.Lewis Jr., W.B. Riesenfeld, J.Math. Phys.10, 1458 (1969).
Antonio B Nassar, J M F Bassalo, H S Antunes Neto, Paulo de Santos Alencar, On the use of space-time transformations in path integration, J.Phys. A; Math .Gen.19(1986) L891-L893.
M. Boudjema-B, T. Boudjedaa, A. Makhlouf. Schwinger action principle via linear quantum canonical transformations, Eur.Phys.J.C46,807-816(2006).
B. K. Cheng, The exact propagator of time-dependent forced harmonic oscillator, J. BrasiIlian Phy, Vol.13, 1, (1983).
R. Cordero-Soto, E. Suazo and S. K. Suslov, Quantum integrals of motion for variable quadratic Hamiltonians, to appear in Annals of Physics, see also arXiv:0912.4900v8 [math-ph] 31 Jan 2010.
