Energy Evolution in Time-Dependent Harmonic Oscillator
نویسندگان
چکیده
منابع مشابه
Energy Evolution in Time-Dependent Harmonic Oscillator
The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general timedependent one-dimensional harmonic oscillator, whose Newton equation q̈+ω(t)q = 0 cannot be solved in general. We follow the time-evolution of an initial e...
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Following a recent work by Robnik and Romanovski (J.Phys.A: Math.Gen. 39 (2006) L35, Open Syst. & Infor. Dyn. 13 (2006) 197-222) we derive the explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t), and is closely related to the conservation of the adiab...
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Abstract. The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework of the technique (Robnik M, Romanovski V G, J. Phys. A: Math. Gen. 33 (2000) 5093) based on WKB approach. Energy evolution for the ensemble of unifo...
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The propagator for a harmonic oscillator with general time-dependent mass and frequency matrices is constructed from the Van-Vleck/Morette formula. The explicit form of the classical action, and thus of the propagator, is found in terms of infinite series which are solutions to a set of differential equations. Those equations are found independently via the Hamilton-Jacobi equation, and by comp...
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The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing quantum-mechanical time evolution in the framework of an extended Hilbert space structure. Physical interpretation of the extended structure has been discussed short...
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ژورنال
عنوان ژورنال: Open Systems & Information Dynamics
سال: 2006
ISSN: 1230-1612,1793-7191
DOI: 10.1007/s11080-006-8222-0