含时阻尼谐振子的传播子与严格波函数

通过正则化变换技巧,寻找到一种对阻尼系数随时间变化的阻尼谐振子直接量子化方案,进而采用高斯型传播子和费曼路径积分方法求出了含时阻尼谐振子的严格波函数,并对波函数的普遍意义,坐标和动量的零点涨落以及两者的不确定关系作了讨论 关键词： 含时阻尼 传播子 费曼路径积分     

质量和频率随时间变化的受迫谐振子的传播子

质量和频率随时间变化的谐振子可描述许多物理系统,研究和求解含时系统在量子场论和量子光学中有重要的意义.本文用SU(1,1)李代数的方法求解了质量和频率随时间变化的谐振子系统.通过求解黎卡提方程,得到系统算符的系数.在相空间推导了体系传播子的计算公式.最后,计算了自由粒子、受重力场驱动、质量随周期变化和阻尼谐振子的传播子.     

一类特殊谐振子问题的路径积分研究

考虑存在耦合,且质量不等的双谐振子系统,利用路径积分的方法研究了该系统的费曼振幅。结果表明,这一系统可以等效为退耦合的双谐振子系统,但退耦合的具体方案不具有唯一性。同时,给出了退耦合后谐振子的等效质量与等效频率。这一基本分析思路有望为解决耦合的多谐振子系统的相关问题提供帮助。     

关于谐振子第一积分的研究

提出一维谐振子基本积分的概念, 并利用它们构造其他积分. 将上述概念和方法推广到多维谐振子, 利用直接构造法证明不同类型的二维谐振子都存在三个与时间无关的独立的第一积分, n维谐振子系统存在2n-1个与时间无关的独立的第一积分. 讨论了分振动频率比为有理数和无理数的二维非对称谐振子的特征. 关键词： 谐振子 第一积分 基本积分 不含时积分     

含时受迫谐振子传播子的精确解

在薛定谔绘景中,运用李代数方法,给出谐振子湮灭算符和产生算符的含时么正线性变换公式,结合含时量子系统的演化方程,得到含时受迫谐振子传播子的精确表达式。     

含时量子系统传播子的ABCD形式

将含时量子系统状态的演化看成物质波波束沿时间轴的传输,引入束宽、发散角、曲率半径、品质因子和束熵表征波束的传输.发现品质因子守恒的量子系统,其动量算子和位置算子呈线性演化,传播子可以表达成ABCD的形式,最小波包(品质因子为1)的形式不随时间改变.讨论了对常数势能系统和谐振子系统的应用 关键词： 物质波束 光束 谐振子     

二模谐振子能谱研究

通过对非耦合谐振子系统能谱、非耦合与坐标耦合共同组成的谐振子系统能谱、非耦合与动量耦合共同组成的谐振子系统能谱、非耦合与坐标动量交叉耦合共同组成的谐振子系统能谱和非耦合与压缩项耦合共同组成的谐振子系统5种谐振子能谱进行求解时,通过分析比较发现:其一,对存在非对易参数的能级差的解时,当非对易参数为零时,所求的哈密顿量能级差的解与非耦合谐振子能谱能级差的解相似,从而验证了求解结果的正确性;其二表明了坐标耦合系数、动量耦合系数和压缩性系数都对共同组成的谐振子系统能谱的能级差产生了影响;其三,对非耦合与坐标动量交叉耦合共同组成的谐振子系统能谱而言,坐标动量交叉耦合系数和非对易参数都没有对交叉耦合谐振子的能级差产生任何影响.对多种耦合系统谐振子能谱进行求解,覆盖面广,分析全面.     

用explicit Euler 方法研究含时受迫谐振子的演化及对系统循环初态的讨论

利用Ioan Sturzu 提出的explicit Euler方法 (EEM) 计算了含时受迫谐振子的系统初态随时间的演化及概率分布规律，分析了EEM的可行性及适用性，并由相干态讨论了受迫谐振子系统循环初态的存在条件以及非绝热几何相. 关键词： explicit Euler 方法 含时受迫谐振子 循环初态 非绝热几何相     

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     

均匀分布费米系统的组态路径积分蒙特卡罗模拟

改进了组态路径积分蒙卡方法,简化采样过程,开发相应程序并对无库伦相互作用谐振子以及均匀电子气进行模拟.谐振子平衡态能量与Fermi-Dirac分布符合较好,均匀电子气平衡态能量和动量基本符合Fermi-Dirac分布规律.对两种费米子系统的研究表明,组态路径积分蒙卡方法对费米子的交换效应具有较好的描述.本文探讨了费米交换符号问题的解决途径,同时对均匀电子气模型进行研究,为后续温热稠密物质的研究奠定基础.     

Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field

In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained.     

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.     

Oscillator with random trichotomous mass

In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

Quantum system driven by periodic external field

A quantum Floquet Theory for a periodically driven system is studied. For this purpose the periodic external fields are changed to have an increasing amplitude with exp(t), where is an infinitestimal positive number to be taken to be zero at the end. By using the expansions in terms of inverse powers of the driving frequency, periodic factors of the time evolution operator are factorized successively. Each step corresponds to a periodically driven system with different strength of external field. This approach produces a time-independent effective Hamiltonian. The effectiveness of the method is examined by applying it to simple models; 1) a forced harmonic oscillator, 2) a particle in the double-well potential, and 3) a hydrogen atom in an electric potential.     

Mean-square displacement of a stochastic oscillator: Linear vs quadratic noise

Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability.     

二维谐振子与加反平方势的二维氢原子的能量关系

通过SU(1,1)代数,找出了二维谐振子与加上反平方势微扰后的二维氢原子的能量对应关系     

Behavioral Differences of a Time-Dependent Harmonic Oscillator in Commutative Space and Non-Commutative Phase Space

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.     

Geometric phases and Mielnik's evolution loops

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called evolution loops). We make a detailed treatment of systems having equally-spaced energy levels. Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found coherent states.