共查询到20条相似文献,搜索用时 46 毫秒
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Ding Sheng R. D. Khan Zhang Jialun Shen Wenda 《International Journal of Theoretical Physics》1995,34(3):355-368
The quantum harmonic oscillator with time-dependent mass and frequency is analyzed by using the canonical transformation method. The varying mass and frequency of the system are reduced to constant mass and frequency, and the corresponding eigenvalues and eigenvectors are derived. The exact time-dependent coherent state of the harmonic oscillator is constructed and shown to be equivalent to the squeezed state. Damped harmonic oscillators with different frictions and forced time-dependent harmonic oscillators are also discussed. 相似文献
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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
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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
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We derive an infinite number of new invariants and related auxiliary equations for the time-dependent harmonic oscillator. 相似文献
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《Physics letters. A》1984,101(9):464-468
Horváthy's modification of Feynman's path integral formula is generalized to the time-dependent forced harmonic oscillator. The propagator at caustics is then obtained by using its modified semi-group property. Finally, with our new formula, the propagator for a charged particle in a time-dependent electromagnetic field is evaluated exactly beyond and at caustics. 相似文献
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含时阻尼线性谐振子的量子不变量处理 总被引:1,自引:0,他引:1
在适当的正则化变换下,采用Lewis-Riesenfeld量子不变量理论,得到了含时阻尼线性谐振子的精确波函数,波函数的正确性和普遍性同样得到讨论. 相似文献
8.
Jeong Ryeol Choi Min-Soo Kim Daeyeoul Kim Mustapha Maamache Salah Menouar In Hyun Nahm 《Annals of Physics》2011,326(6):1381-1393
Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville–von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system. 相似文献
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《Physics letters. A》1987,123(6):297-301
We find the quantum propagator of the harmonic oscillator with a time-dependent mass solving directly the Schrödinger equation through a change of variable and a time reparametrization. 相似文献
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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
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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
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《中国物理 B》2015,(8)
Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket obeying the quadratic time-dependent Hamiltonian(QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific timedependent periodic harmonic oscillator, the Berry phase is obtained exactly. 相似文献
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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
15.
Bin Kang Cheng 《Physics letters. A》1985,113(6):293-296
By finding a space and time transformation, the exact evaluation of the propagator for the harmonic oscillator with a time-dependent mass by the path integral method becomes possible. We then derive the wavefunctions from the propagator obtained. Finally, the propagator beyond and at caustics is evaluated by using its modified semi-group property and is confirmed by investigating the classical paths with two fixed end-positions. 相似文献
16.
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
17.
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
18.
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
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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