Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity

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.     

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.     

Even and Odd Coherent States for Time-Dependent Harmonic Oscillator

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.     

Even and Odd Coherent States for Time-Dependent Harmonic Oscillator

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.     

Forced Time-Dependent Harmonic Oscillator in a Static Magnetic Field: Exact Quantum and Classical Solutions

Exact wave functions of the forced time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived by unitary transformation. The geometrical phase induced by the driving force is the phase of the de Broglie wave associated with the particle moving according to the classical equation. Extending the idea of the Heisenberg correspondence principle to the time-dependent system, the exact classical solution obtained from quantum matrix elements.     

Forced Time-Dependent Harmonic Oscillators in Non-Commutative Space

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.     

Time-Dependent 2D Harmonic Oscillator in Presence of the Aharanov-Bohm Effect

We use the Lewis-Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensionnal harmonic oscillator with time-dependent mass and frequency in presence of the Aharonov-Bohm effect (AB). We find that the auxiliary equation is independent of the AB magnetic flux. In the particular case of quantized AB magnetic flux the wavefunctions coincide exactly with the wavefunctions of the 2D time-dependent harmonic oscillator. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

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 Schrodinger 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 eases 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 some parametric moving boundaries as well.     

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.     

Interpretation of the Quantum Measurement: Example of a Linearly Coupled Harmonic Oscillator

We argue that it may be possible to consistently explain the quantum measurement by assuming that the wave function is in one-to-one correspondence with objective physical reality and has no probabilistic interpretation. In the context of such approach we consider the model of a harmonic oscillator linearly coupled to a heat bath and treat the oscillator as the system being measured. Three classes of initial pure states for the bath are considered. Exact expressions for the average values and variances of the oscillator coordinate and momentum as functions of time are considered for each class of pure states. It is shown that these quantities exhibit different asymptotic behavior for different classes of initial states of the bath. In particular, if each mode of the bath is initially in a coherent state, then for an arbitrary initial state of the oscillator the variances of the oscillator coordinate and momentum asymptotically approach the same values as for a coherent state of the free oscillator, while the averages of coordinate and momentum show a Brownian-like behavior. We argue that such behavior shows several features of the quantum measurement and supports our interpretation of the wave function.     

依赖于时间和强度耦合J-C模型中原子偶极压缩特性

研究了依赖于时间和强度耦合J-C模型中原子的偶极压缩现象。并详细讨论了原子与腔场以时间脉冲形式耦合时,脉冲宽度和腔场强度对原子算符压缩的影响。结果表明,在此模型下原子的偶极压缩随时间的演化特性与其他强度耦合模型明显不同,而且可以通过调节脉冲宽度有效控制原子的偶极压缩程度。     

Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

The stochastic quantization method recently developed by Haba and Kleinert is extended to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization procedure involves the solution of a nonlinear, auxiliary equation. Using a rescaling transformation, the Schrödinger equation for the time-dependent harmonic oscillator is obtained after averaging of a classical stochastic differential equation.     

Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

The stochastic quantization method recently developed by Haba and Kleinert is extended to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization procedure involves the solution of a nonlinear, auxiliary equation. Using a rescaling transformation, the Schrö-din-ger equation for the time-dependent harmonic oscillator is obtained after averaging of a classical stochastic differential equation.     

Exact Solutions with Arbitrary Permutation Symmetry in a Three-Body Harmonic Oscillator

The exact solutions with arbitrary permutation symmetry to the threebody Schrödinger equation for the harmonic oscillator are presented completely.     

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneousstatic electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrodingerequation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. Insome of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherentand squeezed states and their time evolution axe discussed in detail.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrödinger equation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. In some of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherent and squeezed states and their time evolution are discussed in detail.     

非对易空间中耦合谐振子的能级分裂

非对易空间效应的出现引起了物理学界的广泛兴趣。 介绍了非对易空间中量子力学的代数关系,在所考虑的空间变量的对易关系中包含了坐标 坐标的非对易性, 并且把 Moyal-Weyl 乘法在非对易空间中通过一个Bopp变换转变成普通的乘法。 然后给出了非对易空间中耦合谐振子的能级分裂情况。 The effect of noncommutativity of space have caused the physical academic circles widespread interest. In this paper, the non commutative (NC) is introduced, which contain non commutative of coordinate coordinate, and find that the Moyal Weyl product in NC space can be replaced with a Bopp shift. Then, the energy splitting of the coupling harmonic oscillator in non commutative spaces are discussed.     

带电线性谐振子在非对易空间中的Wigner函数

在利用Wigner函数性质的基础上, 考虑到空间变量的对易关系中包含了坐标 坐标的非对易性, 得到了带电线性谐振子在非对易空间中的Wigner函数。 Based on the property of wigner function, the Wigner function of charged Linear Harmonic Oscillator in non commutative space was obtained by considering the noncommutative of the coordinate coordinate in the relation of space variable.