Localization of s-Wave and Quantum Effective Potential of a Quasi-free Particle with Position-Dependent Mass

The properties of the 8-wave for a quasl-free partide with position-dependent mass （PDM） have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle around the origin only occurs in two dimensions, the quasi-free particle with PDM can experience attractive forces in D dimensions except D = 1 when its mass function satisfies some conditions. The effective mass of a particle varying with its position can induce effective interaction, which may be attractive in some cases. The analytical expressions of the eigenfunctions and the corresponding probability densities for the 8-waves of the two- and three-dimensional systems with a special PDM are given, and the existences of localization around the origin for these systems are shown.     

DKP Equation with Smooth Potential and Position-Dependent Mass

The Duffin-Kemmer-Petiau (DKP) equation for spin 0 and 1 with smooth potential and position dependent- mass is solved. The solution is given in terms of the Heun function. The step case for potential and mass are deduced as a limiting case. The boundary conditions are also discussed. PACS Numbers:03.30.+p, 03.65.Pm, 03.65.Ge, 03.65.Db     

Coordinate Transformation and Exact Solutions of Schr(o)dinger Equation with Position-Dependent Effective Mass

Using the coordinate transformation method, we solve the one-dimensional Schr(o)dinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigcnfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.     

Semiclassical Method to Schroedinger Equation with Position-Dependent Effective Mass

In this paper, two novel semiclassical methods including the standard and supersymmetric WKB quantization conditions are suggested to discuss the Schroedinger equation with position-dependent effective mass. From a proper coordinate transformation, the formalism of the Schroedinger equation with position-dependent effective mass is mapped into isospectral one with constant mass and therefore for a given mass distribution and physical potential function the bound state energy spectrum can be determined easily by above method associated with a simple integral formula. It is shown that our method can give the analytical results for some exactly-solvable quantum systems.     

Non-hypergeometric Type of Polynomialsand Solutions of Schrödinger Equation with Position-Dependent Mass

Using the coordinate transformation method, we study the polynomial solutions of the Schrödinger equation with position-dependentmass (PDM). The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The issues related to normalization of the wavefunctions and Hermiticity of the Hamiltonian are also analyzed.     

Generalized Harmonic Oscillator and the SchrSdinger Equation with Position-Dependent Mass

We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.     

Form-Preserving Transformations of Time-Dependent Schrödinger Equation with Time- and Position-Dependent Mass

We study space-time transformations of the time-dependent Schrödinger equation (TDSE) with time- and position-dependent (effective) mass. We obtain the most general space-time transformation that maps such a TDSE onto another one of its kind. The transformed potential is given in explicit form.     

Bound State Solutions of Schrödinger Equation for GeneralizedMorse Potential with Position-Dependent Mass

The effective mass one-dimensional Schrödinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.     

Radiation Reaction of a Nonrelativistic Quantum Charged Particle

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed.     

Series Solution for Localization and Entanglement of an Exciton in a Quantum Dot Molecule by an ac Electric Field

The Schrödinger equation involving the phenomenon of the localization and entanglement for an exciton in a quantum dot molecule by an ac electric field is analytically investigated. New exact series solutions for the Schrödinger equation have been obtained for the first time. The analytical expressions can further describe the dynamical behaviors of an interacting electron-hole pair in a double coupled quantum dot molecule under an ac electric field accurately.     

Localization effects and dispersion of the dielectric response function in one-dimensional metals

We report the results of calculations and analysis concerning the dependence of the dielectric response function(, q) on frequency and wave numberq in one-dimensional conductors. The localization of electron states leads to unusually complicated dependences of(, q) on andq in low-frequency and long-wavelength regions, while the spatial and time dispersions become closely interwoven with each other. The effect of geometric resonance is discussed. It appears as quasiharmonical oscillations of complex susceptibility as function of andq, owing to the hopping nature of electron conductivity in a nonuniform electromagnetic field.     

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.     

Conformal Invariance and a New Type of Conserved Quantities of MechanicalSystems with Variable Mass in Phase Space

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided.Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.     

Steady-State Analysis of a Single-Mode Laser Driven by Colored Pump Noise with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λq between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviors of the stationary distribution Qst(I), the mean (I）, and the variance λ2(0) of the laser intensity. It is shown that cross-correlation intensity λq of the complex quantum noise can induce a first-order-like transition. When the pump noise is colored noise (τ≠0), improving the pump parameters monotonously will make the curves of Qst(I) exhibit reentrant phase transition. The fluctuations of laser intensity are strongly influenced by λq and τ when the laser is operated near or below threshold. Especially when τ≠0, the heights of the peaks of the curves of λ2(0)-α0 and α3(0)-α0, (here a0 is the net gain coefficient) go up as λq increases. However the entire curves λ2(0)-α0 and λ3(0)-α0 are abruptly suppressed when λq = 1, in similarity to phase transition of stationary intensity distribution.     

Chetaev型非完整约束相对运动动力学系统Nielsen方程的Mei对称性和Mei守恒量

研究Chetaev型非完整约束相对运动动力学系统Nielsen方程的Mei对称性和Mei守恒量.对Chetaev型非完整约束相对运动力学系统Nielsen方程的运动微分方程、Mei对称性定义和判据进行具体的研究,得到了Mei对称性直接导致的Mei守恒量的表达式.最后举例说明结果的应用.