oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Noether symmetries and the quantization of a Lienard-type nonlinear oscillator  [PDF]
G. Gubbiotti,M. C. Nucci
Mathematics , 2013,
Abstract: The classical quantization of a Lienard-type nonlinear oscillator is achieved by a quantization scheme (M.C. Nucci. Theor. Math. Phys., 168:997--1004, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schr\"odinger equation. This method straightforwardly yields the correct Schr\"odinger equation in the momentum space (V. Chithiika Ruby, M. Senthilvelan, and M. Lakshmanan. J. Phys. A: Math. Gen., 45:382002, 2012), and sheds light into the apparently remarkable connection with the linear harmonic oscillator.
Quantized symplectic oscillator algebras of rank one  [PDF]
Wee Liang Gan,Nicolas Guay,Apoorva Khare
Mathematics , 2004, DOI: 10.1016/j.jalgebra.2006.06.051
Abstract: A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with U_q(sl_2). We study its representation theory, and in particular, its category O.
On the Canonical Transformation of Time-Dependent Harmonic Oscillator  [PDF]
Akpan N. Ikot,Louis E. Akpabio,Ita O. Akpan,Michael I. Umo,Oladunjoye A. Awoga,Alice B. Nyong
Physics Research International , 2010, DOI: 10.1155/2010/103538
Abstract: We performed a two-variable canonical transformation on the time momentum operator, and without loss of generality we carried out a three-variable transformation on the coordinate and momentum space operators to trivialize the Hamiltonian operator of the system. Fortunately, this operation separates the time-coordinate and space coordinate naturally, and the wave function of the time-dependent Harmonic Oscillator is evaluated via the generator.
Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator  [PDF]
M. Fernandez Guasti,H. Moya-Cessa
Physics , 2002, DOI: 10.1103/PhysRevA.67.063803
Abstract: The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time dependent harmonic oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example.
Time-dependent driven anharmonic oscillator and the adiabaticity  [PDF]
Hyeong-Chan Kim,Jae Hyung Yee
Physics , 2002, DOI: 10.1103/PhysRevA.66.032117
Abstract: We use the Liouville-von Neumann (LvN) approach to study the dynamics and the adiabaticity of a time-dependent driven anharmonic oscillator as an eample of non-equilibrium quantum dynamics. We show that the adiabaticity is minimally broken in the sense that a gaussian wave-packet at the past infinity evolves to coherent states, however slowly the potential changes, its coherence factor is order of the coupling. We also show that the dynamics are governed by an equation of motion similar to the Kepler motion which satisfies the angular momentum conservation.
Exact wave function of the coupled harmonic oscillator with time-dependent mass and frequency
质量和频率均含时的耦合谐振子的严格波函数

Ling Rui-Liang,Feng Jin-Fu,
凌瑞良
,冯金福

物理学报 , 2009,
Abstract: Using the coordinate and momentum transformation theory and the trial function methed, the exact wave function of the coupled harmonic oscillator with time-dependent mass and frequency is derived.
Momentum Dependent Fundamental Action  [PDF]
Karl De Paepe
Physics , 2005,
Abstract: The fundamental action is dependent on momentum. Some consequences are presented for matter waves and scalar quantum field theory.
Quantized Excitation Spectrum of the Classical Harmonic Oscillator in Zero-Point Radiation  [PDF]
Wayne Cheng-Wei Huang,Herman Batelaan
Physics , 2012,
Abstract: We report that upon excitation by a single pulse, the classical harmonic oscillator immersed in classical electromagnetic zero-point radiation, as described by random electrodynamics, exhibits a quantized excitation spectrum in agreement to that of the quantum harmonic oscillator. This numerical result is interesting in view of the generally accepted idea that classical theories do not support quantized energy spectra.
Quantized Adiabatic Transport in Momentum Space  [PDF]
Derek Y. H. Ho,Jiangbin Gong
Physics , 2012, DOI: 10.1103/PhysRevLett.109.010601
Abstract: Though topological aspects of energy bands are known to play a key role in quantum transport in solid-state systems, the implications of Floquet band topology for transport in momentum space (i.e., acceleration) are not explored so far. Using a ratchet accelerator model inspired by existing cold-atom experiments, here we characterize a class of extended Floquet bands of one-dimensional driven quantum systems by Chern numbers, reveal topological phase transitions therein, and theoretically predict the quantization of adiabatic transport in momentum space. Numerical results confirm our theory and indicate the feasibility of experimental studies.
On the Canonical Transformation of Time-Dependent Harmonic Oscillator  [PDF]
Akpan N. Ikot,Louis E. Akpabio,Ita O. Akpan,Michael I. Umo,Oladunjoye A. Awoga,Alice B. Nyong
Physics Research International , 2010, DOI: 10.1155/2010/103538
Abstract: We performed a two-variable canonical transformation on the time momentum operator, and without loss of generality we carried out a three-variable transformation on the coordinate and momentum space operators to trivialize the Hamiltonian operator of the system. Fortunately, this operation separates the time-coordinate and space coordinate naturally, and the wave function of the time-dependent Harmonic Oscillator is evaluated via the generator. 1. Introduction The method of Canonical transformations (CT) has proved to be a fruitful approach in treating quantum systems [1]. It is often used in describing systems with Hamiltonian that are quadratic either in co-ordinate and momentum or equivalently in Boson creation and annihilation operators. One major advantage of the method of (CT) consists in reducing the Hamiltonian of the system to a Hamiltonian of some simple system with known solution, that is, . These two systems are canonically equivalent since their Hamiltonian is related by means of a CT. However, analytical approaches to isolate conserved quantities for a given physical system are a major objective in the realm of Hamiltonian theory [2]. For autonomous, where the Hamiltonian is time independent, one conserved quantity is immediately found: the Hamiltonian which represents the total energy of the system is a constant of motion. Rather unfortunately the Hamiltonian of most real physical systems is explicitly time-dependent and does not provide direct conserved quantity. In classical mechanics, the equation of motion governed the dynamical behavior of the system and this second-order differential equation is solved directly by the trivialization of the conjugate variables through CT [3]. Park [3] asserted that because of the non-commutability of operators, CT has not been fully realized in quantum mechanics. However, CT is usually defined as a change of the noncommutating variables that preserved the commutation relations in quantum mechanics [4]. In literature [4, 5] three types of transformations have been identified such as interchange, similarity, and point transformations. Different models of oscillators have been evaluated via the CT [6, 7]. The applications of quantum canonical transformation to a harmonic oscillator in which the angular frequency and equilibrium position are time dependent have been reviewed [3]. In this paper we extend the work of [3] by performing a three-variable transformation on both the space co-ordinate and momentum co-ordinate operators. 2. Time-Dependent Harmonic Oscillator The Time-Dependent Schrodinger Wave
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.