量子动边界广义含时谐振子之精确的指数-正弦型演化态

研究了被局限于区间[0,L(t)]中运动的动边界广义含时谐振子量子系统,其Hamiltonian为坐标与动量的非齐次含时二次型.求出了具有“指数-正弦型”演化态的充要条件以及相应的正交归一完备的精确演化态系列.此结果不但几乎包含了已有结果作为特例,还涵盖了相当广泛的范围.此外,澄清了个别作者关于对时间的微商的一个误解,指出对时-空坐标的微商均具有寻常的含义. 关键词： 动边界量子系统 广义含时谐振子 演化态 精确解     

含时谐振子的动力学演化

利用含时量子变换理论,由量子变换理论中的变换矩阵,方便地给出了含时谐振子的演化算符,从而求得了含时谐振子的精确解. 关键词： 含时谐振子 含时量子变换 动力学演化     

质量和频率随时间变化的谐振子的经典和量子精确解

对质量和频率含时的谐振子用新的简单方法分别求出了其经典运动方程和量子薛定谔方程的精确解。     

广义含时谐振子系统的精确解和压缩态

利用一系列幺正变换,求出了广义含时谐振子系统的精确解,并利用此精确解构造了此系统的压缩态。     

强磁场中碱金属原子的演化和Aharonov－Anandan相因子

利用量子不变量理论研究了任意随时间变化的强磁场中碱金属原子系统的演化问题，得到了此系统精确的演化态，并利用此精确的演化态求出了相应的Ａｎａｒｏｎｏｖ－Ａｎａｎｄａｎ相因子和绝热极限下的Ｂｅｒｒｙ相因子。将此系统精确的演化态按哈密顿量的瞬时本征态展开，可以得到绝热近似的任意阶修正。     

强磁场中碱金属原子原演化和Aharonov—Anandan相因子

利用量子不变量理论研究了任意随变化的强磁场中碱金属原子系统的演化问题，得到了此精确的演化态，并利用此精确的演化态求出了相应的Ａｈａｒｏｎｏｖ－Ａｎａｎｄａｎ相因子和绝热极限下的Ｂｅｒｒｙ相因子。将此系统精确的演化按哈密顿量的瞬音本征态展开，可以得到绝热近似似的任意阶修正。     

具有坐标和动量一阶耦合的两量子谐振子的演化

提出了具有坐标和动量一阶耦合的两量子谐振子的演化问题。通过引起适当的算符和辅助函数，求出了问题的精确解。     

具有q^4的两个耦合量子非谐振子的演化

在文献（５）的基础上，分析了两个耦合的量子非谐振子，并讨论了一种典型的实例，通过引进几个算符和辅助函数，求出了问题的精确解。     

交变电源作用下介观电感耦合电路中电荷与电流的量子涨落

利用量子厄米不变量理论,我们研究了交变电源作用下介观电感耦合电路的量子动力学,不仅得到了含时薛定谔方程的精确解,计算了电路中电荷与电流的量子涨落,同时也得到了介观电路的非绝热非循环几何相位的表达式.     

含时耦合谐振子体系的动力学演化

利用含时量子变换理论,给出含时双模耦合谐振子的严格解.并根据这一结果,对于给定的初态为Fock态和相干态情形,讨论了其动力学演化.     

考虑弹簧质量的振子精确解

给出了考虑弹簧质量时弹簧振子系统频率的精确解，指出了近似解的实质是假设弹簧的位移模式为线性模式，而其实解的位移模式为正弦曲线；算例的结果显示，通常情况下，精确解的一阶位移模式与线性模式非常接近，因此近似解具有相当的精度．     

The Exact Solution,Berry's Phase and Coherent State for the Driven Generalized Time-Dependent Harmonic Oscillator

The Lewis'invariant and exact solution for the driven generalized time-dependent harmonic oscillator is found by making use of the Lewis-Riesenfeld quantum theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry's phase for thirr system is obtained. We then proceed to use the exact solution to construct the coherent state and calculate the corresponding exact classical phase angle. This phase angle can give the Hannay's angle in the adiabatic limit. The relation between the exact Lewis'phase and the corresponding classical phase angle L'discusrred.     

BERRY PHASES IN THE QUANTUM STATE OF THE ISOTROPIC HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

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.     

热库中振子弛豫过程的精确解

本文从VonNeumanm方程出发,求出了热库中振子跃迁几率的精确解。在不作弱耦合近似情况下得到了平衡态分布的形式。 关键词：     

具有含时频率和边界条件的谐振子量子态的Berry相位

对具有一运动边界的一维无限深势阱内频率随时间变化的谐振子的含时Schrdinger方程连续进行两次规范变换，可以得到精确解和Lewis不变量算符.基于该精确解利用几何距离和曲线的几何长度概念计算了体系量子态的Berry相位. 关键词：     

Evolution of a velocity-dependent quantum forced anharmonic oscillator

The exact solution to a velocity-dependent quantum forced anharmonic oscillator is derived by using integral operators and an iteration method. The study is carried out in operational form by use of the creation and annihilation operators of the oscillator. The time development of the displacement and momentum operators of the anharmonic oscillator is given. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals.     

Study of Certain Aspects of Anharmonic,Time-Dependent and Damped Harmonic Oscillator Systems

The present review is devoted to the study of certain aspects of anharmonic, time-dependent and damped oscillator(s) system using different theoretical techniques. A theoretical understanding of these systems is important for application in many problems in physics, mechanics and other fields. We discuss in detail the difficulties in the theoretical analysis of the problem. In particular we discuss here the regular, well-behaved perturbative solution, the large quantum number behaviour of anharmonic oscillator(s) using the technique of coherent states, exact solution of quantum anharmonic oscillators, the electromagnetic radiation emitted by a charged particle executing damped anharmonic oscillator motion using Krylov-Bogoliubov approximation method, use of invariants to obtain solution and coherent states of time-dependent oscillator(s), the derivation of perturbative frequencies of a damped coupled anharmonic oscillators system using suitable canonical transformation in the framework of Hamilton-Jacobi formalism and the quantisation and construction of coherent states of a damped oscillator using time-dependent operators.     

Oblate high spin isomer

Energies of high spin states are calculated with the use of an oblate deformed oscillator potential with the purpose of finding possible yrast traps or isomers. Pairing forces are included and different methods of solving the pairing Hamiltonian (including the exact solution) are compared. The stability of the oblate regime against gamma vibrations is investigated with use of the random phase approximation. Pairing forces are included also here.     

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for someparametric moving boundaries as well.     

Quantum and Classical Exact Solutions of Harmonic Oscillator in a Time-Dependent Magnetic Field

In cylindrical coordinate, exact wave functions of the two-dimensional time-dependent harmonic oscillator in a time-dependent magnetic field are derived by using the trial function method. Meanwhile, the exact classical solution as well as the classical phase is obtained too. Through the Heisenberg correspondence principle, the quantum solution and the classical solution are connected together.