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1.
The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the
classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states
for time-dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a
demonstration of our general approach. 相似文献
2.
In this article, behavioral differences of time-dependent harmonic oscillator in Commutative space and Non-Commutative phase space have been investigated. The considered harmonic oscillator has a time-dependent angular frequency and mass which are function of time. First, the time-dependent harmonic oscillator is studied in commutative space, then similar calculation is done for considered harmonic oscillator in Non-Commutative phase space. During this article method of Lewis–Riesenfeld dynamical invariant has been employed. 相似文献
3.
研究了频率随时间变化的受迫谐振子系统的不变量和不变量的一般形式,并利用基本不变量构造了此含时系统的压缩态和压缩数态. 相似文献
4.
H.J. Korsch 《Physics letters. A》1979,74(5):294-296
A simplified algebraic derivation of the dynamical (Lewis) invariant for the time-dependent harmonic oscillator is presented. The treatment is based on the concept of the dynamical algebra. 相似文献
5.
Jeong-Ryeol Choi 《Pramana》2003,61(1):7-20
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic
oscillator. The uncertainty relation of the system is always larger than ħ/2 not only in number but also in the thermal state
as expected. We used the diagonal elements of density operator satisfying Leouville-von Neumann equation to calculate various
expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola-Kanai oscillator. 相似文献
6.
In this contribution, we investigate quantum effects of relic gravitons in a Friedmann–Robertson–Walker (FRW) cosmological background. We reduce the problem to that of a generalized time-dependent harmonic oscillator and find the corresponding exact Schrödinger states with the help of linear invariants and of the dynamical invariant method. Afterwards, we construct Gaussian wave packet states and calculate the quantum dispersions as well as the quantum correlations for each mode of the quantized field. 相似文献
7.
二维各向同性变频率谐振子的超对称性及其不变量的超对称量子力学精确解 总被引:1,自引:0,他引:1
采用超对称量子力学与不变量相结合的方法讨论了二维各向同性变频率谐振子,给出了二维各向同性变频率谐振子的不变量,采用超对称量子力学方法精确求解了不变量的本征值和本征函数,并且给出了当频率恒定时,二维常频率谐振子的本征值和本征函数的精确解.最后对不变量的超对称性进行了讨论. 相似文献
8.
Jeong Ryeol Choi 《Pramana》2004,62(1):13-29
By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator.
The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai
oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude
of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant
frequency oscillates with a large amplitude, even after a sufficient time elapse. 相似文献
9.
For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtained as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space. 相似文献
10.
Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions 下载免费PDF全文
We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D(D ≥ 1) dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated. 相似文献
11.
In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the generalized time-dependent forced harmonic oscillator in terms of solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations between coordinate and momentum. It is shown that the width of the Gaussian packet, fluctuations and correlations do not depend on the external force. As a particular case, we consider the forced Caldirola-Kanai oscillator. 相似文献
12.
受与速度平方成正比的力的变频率谐振子(THOFQV)可以用一个适当的Lagrangian量来描述,可以求出THOFQV的普遍解.再利用不变量算子求解该系统的Schrdinger方程,得到本征函数和本征值.
关键词:
谐振子
不变量
本征函数
本征值 相似文献
13.
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity isobtained by making a specific coordinate transformation and by using the method of time-dependent invariant. 相似文献
14.
Daniel Gómez Vergel 《Annals of Physics》2009,324(6):1360-1385
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a single one-dimensional time-dependent oscillator, for which we first summarize some basic results concerning the unitary implementability of the dynamics. This is done by employing techniques different from those used so far to derive the Feynman propagator. In particular, we calculate the transition amplitudes for the usual harmonic oscillator eigenstates and define suitable semiclassical states for some physically relevant models. We then explore the possible extension of this study to infinite dimensional dynamical systems. Specifically, we construct Schrödinger functional representations in terms of appropriate probability spaces, analyze the unitarity of the time evolution, and probe the existence of semiclassical states for a wide range of physical systems, particularly, the well-known Minkowskian free scalar fields and Gowdy cosmological models. 相似文献
15.
Victor V. Dodonov 《Journal of Russian Laser Research》2010,31(2):152-161
A “microscopic” justification of the “symmetric damping” model of a quantum oscillator with time-dependent frequency and time-dependent
damping is given. This model is used to predict the results of experiments on simulating the dynamical Casimir effect in a
cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a
selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both
quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration
is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads
to the “minimum noise” model of the quantum damped oscillator, introduced earlier in a pure phenomenological way. 相似文献
16.
Gauge covariant construction of the coherent states for a time-dependent harmonic oscillator by algebraic dynamical method 总被引:5,自引:0,他引:5
Lian-Fu Wei Shun-Jin Wang Quan-Lin Jie 《Zeitschrift für Physik B Condensed Matter》1997,102(4):541-543
Time-dependent coherent states for a time-dependent harmonic oscillator are constructed in the framework of algebraic dynamics. These coherent states are gauge-covariant, and its time evolution is governed only by the solutions of a linear differential equation which describes the motion of the corresponding classical timedependent harmonic oscillator. Its non-classical and quantum statistical properties can thus be controlled by a proper choice of the frequency of the harmonic oscillator. Our coherent states reduce to Glauber coherent states in the case as the frequency is independent of time. 相似文献
17.
C. F. Lo 《Il Nuovo Cimento D》1991,13(10):1279-1292
Summary In this paper we investigate the time evolution of a general driven time-dependent oscillator using the evolution operator
method developed by Chenget al. We obtain an exact form of the time evolution operator which, in turn, enables us to find the exact wave functions and coherent
states at any timet. Our analyses indicate that the time-dependent coherent state is equivalent to the well-known squeezed state, while the time-dependent
number state is equivalent to the displaced and squeezed number state. Besides, we also calculate the time-dependent transition
probabilities among the coherent states and number states of a simple harmonic oscillator associated with the initial HamiltonianH(0). 相似文献
18.
A generalized two-mode harmonic oscillator model is investigated within the framework of its general dynamical algebra so(3,2). Two types of eigenstates, formulated as extended su(1,1), su(2) squeezed number states are found respectively. The nonadiabatic Berrys phase for this system with the cranked time-dependent Hamiltonian is also given.Received: 16 January 2004, Published online: 10 August 2004PACS:
42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements - 03.65.Fd Algebraic methods - 03.65.Vf Phases: geometric; dynamic or topological 相似文献
19.
BERRY PHASES IN THE QUANTUM STATE OF THE ISOTROPIC HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS 下载免费PDF全文
The problem of the isotopic harmonic oscillator of time-dependent frequency confined in a spherical box with time-dependent radius is studied. We show that the exact solution and the Lewis invariant operator can be obtained by performing two consecutive gauge transformations on the time-dependent Schr?dinger equation. On the basis of the exact solution the non-adiabatic Berry phases for the system are calculated. 相似文献
20.
M. Boudjema-Bouloudenine T. Boudjedaa A. Makhlouf 《The European Physical Journal C - Particles and Fields》2006,46(3):807-816
We have applied the Schwinger action principle to general one-dimensional (1D), time-dependent quadratic systems via linear
quantum canonical transformations, which allowed us to simplify the problems to be solved by this method. We show that while
using a suitable linear canonical transformation, we can considerably simplify the evaluation of the propagator of the studied
system to that for a free particle. The efficiency and exactness of this method is verified in the case of the simple harmonic
oscillator. This technique enables us to evaluate easily and immediately the propagator in some particular cases such as the
damped harmonic oscillator, the harmonic oscillator with a time-dependent frequency, and the harmonic oscillator with time-dependent
mass and frequency, and in this way the propagator of the forced damped harmonic oscillator is easily calculated without any
approach.
PACS 02.30.Xx, 03.65.-w, 03.65.Ca 相似文献