Force acting on an atom and a classical oscillator in an electromagnetic field

The expression for the force exerted by the field on an atom and averaged over the field period is derived in quantum-mechanical perturbation theory, in which a quasi-monochromatic electromagnetic field plays the role of a perturbation. An approximate solution is obtained to the classical (Newton) equation of motion in the same field for a harmonic isotropic oscillator. In both problems, the expressions for the force acting on a particle are completely identical if they are written in terms of the polarizability (of the atom and the oscillator). These results conform with the data obtained in macroscopic electrodynamics for rarefied media.     

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm(AB) flux fields on the energy levels of a two-dimensional(2D) Klein-Gordon(KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator(PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov(NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.     

外加磁场下抛物型量子线中的带电激子

在一维等效模型下采用有效差分法对抛物型量子阱线中带电激子的束缚能进行了计算,分析了约束势以及磁场对带电激子束缚能的影响,并对带正电激子(X⁺)和带负电激子(X^-)的情况进行了比较.结果表明:电子和空穴的振子强度对带电激子的稳定性有重要影响,X⁺的束缚能不总是比X^-的大,随着空穴振子强度的增加束缚能的函数曲线将会出现交叉,这同实验得到的结果符合;磁场的存在会增加粒子间的束缚,并且磁场对束缚能的影响同振子强度大小有关. 关键词： 带电激子 量子线 束缚能 磁场     

Time Dependence of Joint Entropy of Oscillating Quantum Systems

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.     

One-parameter Lie groups admitted by time-dependent Schrödinger equation: Atoms,molecules and nucleons in harmonic oscillator field

Lie’s method of differential equation is used to obtain the one-parameter Lie groups admitted by the time-dependent Schrödinger equations for atoms, molecules and nucleons in harmonic oscillator field. This group for atoms and molecules is isomorphic to 10-parameter inhomogeneous orthogonal group in 4 dimensions, irrespective of the numbers of nuclei and electrons. For Z protons andN neutrons in a harmonic oscillator field, both isotropic and anisotropic, the r-parameter Lie groups are seraidirect products of an invariant subgroup and a factor group. In the case of isotropic oscillator field r is 1/2[3Z(3Z-1) +3N (3N -1)+2], while for the anisotropic oscillator field r is 1/2[3Z (Z+1)+3N(JV+1)+2].     

One Dimensional Models with a Singular Potential of the Type −<Emphasis Type="Italic">αδ</Emphasis>(<Emphasis Type="Italic">x</Emphasis>)+<Emphasis Type="Italic">βδ</Emphasis>′(<Emphasis Type="Italic">x</Emphasis>)

We study a one-dimensional singular potential plus two types of regular interactions: constant electric field and harmonic oscillator. In order to search for the bound state energies, we shall use the Lippman-Schwinger Green function technique. Another direct method will be mentioned for the harmonic oscillator. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy “quasibound states” appear. The harmonic oscillator demonstrates the general result that for a symmetric potential the odd states are not altered whereas the even states energies are lowered or raised accordingly as the delta perturbation is attractive or repulsive. No states are created or annihilated.     

Power Series Expansion of Propagator for Path Integral and Its Applications

In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.     

推广的Glauber理论及其在晕核散射中的应用

介绍了推广到晕核散射的Glauber理论,并用其研究晕核¹⁴Be的散射问题.弹核的密度分布分别采用谐振子密度分布和相对论平均场理论计算得到具有两个晕中子结构的密度分布,对晕核模型的多重积分采用蒙特卡洛数值积分方法.计算了不同能量下¹⁴Be,¹²Be与靶核¹²C散射的反应截面,并与实验结果进行比较,¹⁴Be的两个中子采用具有晕中子密度分布的理论计算与实验符合较好,而采用不具有晕中子密度分布的结果与实验值相差较大.     

Pseudospin symmetry and the relativistic ring-shaped non-spherical harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The eigenfunctions and eigenenergies are obtained for the ring-shaped non-spherical harmonic oscillator by solving Dirac equation with equal mixture of vector and scalar potentials in opposite signs, for which pseudospin symmetry is exact. Several particular cases such as the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

The analytical transfer matrix method for quantum reflection

In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech$^{2}$ barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 \wx{Quantum Mechanics (Non-relativistic Theory)}{} (New York: Pergamon)], which proves that ATMM is a simple and effective method for quantum reflection.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

Dynamics of a Quantum Damped Oscillator with Relaxation

The quantum problem of a nonlinear oscillator interacting with the field of harmonic oscillators with continuously distributed frequencies is examined. The Heisenberg representation is used. It is demonstrated that after elimination of field variables from the equation, the oscillator dynamics is described by an integro-differential operator equation. It is proved that in the general nonlinear case, an exact solution for the quantum oscillator demonstrates dissipative behavior under certain limitations on the relaxation kernel.     

谐振子薛定谔方程的简单解法

物质的许多物理与化学性质都可以用线性谐振子模型解释，本文用简单的数学运算求解线性谐振子的薛定谔方程，避免了特殊函数等复杂的数学运算，得出了量子力学教材完全相同的结果。     

(ZnSe)_(12)在外电场下的基态性质和激发特性研究

以SBKJC为基组,采用密度泛函PBE0方法研究了不同外电场(0-0.030 a.u.)对(ZnSe)_(12)的基态几何结构、电荷分布、能量、电偶极矩、能隙、最小振动频率的影响;继而采用含时的TD-PBE0方法研究了(ZnSe)_(12)在外电场下的激发特性,并模拟了紫外-可见光谱.研究结果表明:外电场的加入导致分子对称性降低,当电场从0 a.u.变化到0.030 a.u.时,偶极矩逐渐增加,体系总能量、最小谐振频率和能隙一直减小.外电场对(ZnSe)_(12)的激发特性影响较大,随着电场的增加,紫外-可见光谱发生红移,同时对振子强度有很大影响,原来振子强度不为零的激发态变弱或成为禁阻跃迁,而原来振子强度很弱或禁阻的激发态变得很强.可以通过改变外电场来改变(ZnSe)_(12)的基态性质,以及控制(ZnSe)_(12)的吸收和发光特性.     

阻尼谐振子的严格波函数

对与速度成正比的阻尼谐振子，通过正则变换，采用路径积分方法，得出了阻尼谐振子的严格波函数，还讨论了阻尼谐振子的坐标、动量的零点涨落. 关键词：     

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.     

阻尼谐振子的拉格朗日函数和哈密顿函数

利用一种直接方法将阻尼谐振动微分方程变换成等价的自伴随形式,并构造出阻尼振子的两个拉格朗日函数和哈密顿函数,导出了阻尼谐振子的Noether守恒量.     

The residue harmonic balance for fractional order van der Pol like oscillators

When seeking a solution in series form, the number of terms needed to satisfy some preset requirements is unknown in the beginning. An iterative formulation is proposed so that when an approximation is available, the number of effective terms can be doubled in one iteration by solving a set of linear equations. This is a new extension of the Newton iteration in solving nonlinear algebraic equations to solving nonlinear differential equations by series. When Fourier series is employed, the method is called the residue harmonic balance. In this paper, the fractional order van der Pol oscillator with fractional restoring and damping forces is considered. The residue harmonic balance method is used for generating the higher-order approximations to the angular frequency and the period solutions of above mentioned fractional oscillator. The highly accurate solutions to angular frequency and limit cycle of the fractional order van der Pol equations are obtained analytically. The results that are obtained reveal that the proposed method is very effective for obtaining asymptotic solutions of autonomous nonlinear oscillation systems containing fractional derivatives. The influence of the fractional order on the geometry of the limit cycle is investigated for the first time.     

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.     

Hyperspherical harmonics and the nuclear four-body problem

A method proposed earlier by Aguilera, Moshinsky, and Kramer, for adapting a system of translationally invariant four-particle harmonic oscillator functions to the symmetry of the permutation group S(4), is applied to hyperspherical harmonic functions depending on three relative vectors. Except for a few cases in which diagonalization of matrices is required, the method gives closed formulas for orthonormal sets of harmonic functions with good permutational symmetry. The matrix elements of S(4) permutations with respect to the harmonic functions are obtained.