Cosmological Wave Function and Wormhole Wave Function with a Conformal Complex Scalar Field

Quantum cosmology and the quantum wormhole witha conformal complex scalar field are discussed, thecorresponding Wheeler-DeWitt equations are obtained, andthe cosmological wave functions and wormhole wave functions are calculated, respectively,with different boundary conditions. From thecosmological wave function it is found that theprobability density of the universe is zero at a = 0,while at the ground state the most probable radius is aboutthe Planck scale. It is also shown that there exist twodifferent types of universes, which can be connected bythe quantum tunneling effect, transiting from one region to another. It follows from thewormhole wave function that the most probable radius ofthe wormholes is about the Planck scale, which impliesthat the wormhole is steady due to the quantumeffect.     

Global Phase Time and Wave Function for the Kantowski-Sachs Anisotropic Universe

A consistent quantization with a clear notion of time and evolution is given for the anisotropic Kantowski–Sachs cosmological model. It is shown that a suitable coordinate choice allows to obtain a solution of the Wheeler–DeWitt equation in the form of definite energy states, and that the results can be associated to two disjoint equivalent theories, one for each sheet of the constraint surface.     

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.     

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopic mapping method.     

缀饰原子的简化波函数(英文)

作为含时薛定谔方程的微扰近似解,在速度规范下给出了激光场中缀饰原子的一个波函数.利用平均激发能近似和完备关系,可将此波函数简化为一个含时的相乘算符作用于无场时的"裸原子"态上.在软光子近似下,平均激发能仅出现在光场频率的一阶和二阶项上.此波函数适用于计算激光辅助的散射过程,特别是重排过程. A wave function for laser dressed atom is derived as a perturbative solution of the time dependent Schrdinger equation in the velocity gauge. With the use of the average excitation energy approximation and the closure approximation, the solution is reduced to a time dependent operator acting on the "bare" atomic state. In soft photon approximation, the average excitation energy only appears in the first and second order terms of field frequency. Such a simplified dressed wave function is useful in...     

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.     

Elliptic Equation and Its Direct Applications to Nonlinear Wave Equations

Elliptic equation is taken as an ansatz and applied to solve nonlinear wave equations directly. More kinds of solutions are directly obtained, such as rational solutions, solitary wave solutions, periodic wave solutions and so on. It is shown that this method is more powerful in giving more kinds of solutions, so it can be taken as a generalized method.     

Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.     

The Peridic Wave Solutions for Two Nonlinear Evolution Equations

By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.     

Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic: equation is taken as a transformation and is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.     

The Periodic Wave Solutions for Two Nonlinear Evolution Equations

By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobi elliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.     

Periodic Wave,Solitary Wave and Compacton Solutions of a Nonlinear Wave Equation with Degenerate Dispersion

In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.     

Shape Analysis and Solution to a Class of Nonlinear Wave Equation with Cubic Term

In this paper, we analyze the relation between the shape of the bounded traveling wave solutions and dissipation coefficient of nonlinear wave equation with cubic term by the theory and method of planar dynamical systems. Two critical values which can characterize the scale of dissipation effect are obtained. If dissipation effect is not less than a certain critical value, the traveling wave solutions appear as kink profile; while if it is less than this critical value, they appear as damped oscillatory. All expressions of bounded traveling wave solutions are presented, including exact expressions of bell and kink profile solitary wave solutions, as well as approximate expressions of damped oscillatory solutions. For approximate damped oscillatory solution, using homogenization principle, we give its error estimate by establishing the integral equation which reflects the relations between the exact and approximate solutions. It can be seen that the error is an infinitesimal decreasing in the exponential form.     

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.     

Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations

The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi elliptic cosine function and the third elliptic function solutions are obtained. It is shown that the shock wave solutions and solitary wave solutions can be obtained at their limit condition.     

Soliton and Rogue Wave Solution of the New Nonautonomous Nonlinear Schrödinger Equation

In this paper, a new type (or the second type) of transformation which is used to map the variable coefficient nonlinear Schrödinger (VCNLS) equation to the usual nonlinear Schrödinger (NLS) equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is
introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically.
The main differences between the two types of transformation mentioned above are listed by three items.     

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.     

Effective Action for a Statistical System with a Field Dependent Wave Function

We compute the first order correction in ħ to the field dependent wave function in Statistical Field Theory. These corrections are evaluated by several usual methods. We limit ourselves to a one dimensional model in order to avoid the usual difficulties with the UV divergences that are not relevant for our purposes. The main result of the paper is that the various methods yield different corrections to the wave function. Moreover, we give arguments to show that the perturbative integration of the exact renormalization group provides the right result.