具有非局域势的量子力学模型

利用超对称性(SUSY)量子力学讨论能够精确求解的具有非局域势的量子力学模型.并表示出能够精确求解的局域势模型的一个简单非局域的表示形式,精确地得到能量本征函数和本征值.     

The supersymmetric WKB approximation for Hartmann potential

Using the method of supersymmetric WKB approximation, the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions. We take the Hartmann potential as an important example for its validation, and the result is consistent with that obtained by using the supersymmetric quantum mechanics and shape invariance.     

Solving Two Kinds of JC Models Relating to Two-Photon Process by Supersymmetric Transformation

We propose two kinds of new Jaynes Cummings models relating to two-photon process by using the supersymmetric unitary transformation. The corresponding energy eigenvalues and eigenvectors are obtained.     

Solving Two Kinds of JC Models Relating to Two-Photon Process by Supersymmetric Transformation

We propose two kinds of new Jaynes Cummings models relating to two-photon process by using the supersymmetric unitary transformation. The corresponding energy eigenvalues and eigenvectors are obtained.     

The supersymmetric WKB approximation of ring-shaped oscillator potential in r and θ dimensions with spherical polar coordinates

According to calculation of the energy spectrum of ring-shape oscillator potential by using the supersymmetric WKB approximation, it is shown that the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions by above method.     

NEW EXACTLY SOLVABLE SUPERSYMMETRIC PERIODIC POTENTIALS

Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of one-dimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schr?dinger equation for this potential is named the Mathieu equation mathematically. We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.     

Supersymmetric Electroweak Corrections to Top Quark Production at LHC

The am_t²/m²w order supersymmetric electroweak corrections arising from loops of chargino, neu tralino and squark to top quark pair production by gg fusion at LHC are calculated in the minimal supersymmetric model. We found that the corrections amount about a few percent.     

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates,and time evolution of state vector are obtained.     

Solving Multiphoton Jaynes–Cummings Model with Field Nonlinearity by Supersymmetric Unitary Transformation

We introduce a supersymmetric unitary transformation, to diagonalize the multiphoton Jaynes–Cummings model Hamiltonian based on supersymmetric quantum mechanics theory, that includes any forms of intensity-dependent coupling and field nonlinearity. On doing so, we obtain its eigenvalue and eigenstates, and the time evolution of state vector.     

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transformation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates, and time evolution of state vector are obtained.     

Darboux transformations of the Supersymmetric BKP hierarchy

In this paper, we construct Darboux transformations of the supersymmetric BKP(SBKP) hierarchy. These Darboux transformations can generate new solutions from seed solutions by using bosonic eigenfunctions.     

Angular Momentum of Supersymmetric Non-isotropic Traps

A simple way to explain quantum behavior of supersymmetric non-isotropic traps is proposed in the framework of semiunitary formulation of supersymmetric quantum mechanics. Using semiunitary formulation we can simultaneously supersymmetrize the complete set of observables, especially including angular moment.     

MULTIPHOTON JAYNES-CUMMINGS MODEL SOLVED VIA SUPERSYMMETRIC UNITARY TRANSFORMATION

For multiphoton Jaynes-Cummings(JC) model Hamiltonian, we find its supersymmetric structure. Based on this, we introduce a supersymmetric unitary transformation to diagonalize the JC Hamiltonian, in so doing, its eigenvalues and eigenfunctions are obtained. The transition process is also calculated.     

SUPERSYMMETRIC SU(1|2) GAUDIN MODEL

In this paper, we propose a supersymmetric SU(1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.     

超对称准经典近似和本征值问题

运用超对称准经典近似方法给出三维谐振子、氢原子的能谱,进而将该方法用于含角坐标的二阶微分方程,得到角动量平方L2的本征值和非中心势的角向本征值.     

多光子集体辐射原子的J-C模型超对称求解

根据已有的双光子情形具有两个集体辐射原子的Jaynes-Cumm ings(J-C)模型,将之推广到多光子情形。找出了该模型的超对称生成元,然后用超对称变换的方法十分简洁地求解出了它的能量本征值和能量本征态。     

The q-Deformation of the Superoscillators and Their q-Supercoherent States

We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well.     

Supersymmetry and Shape Invariance of Hartmann Potential and Ring-Shaped Oscillator Potential in the γ and θ Dimensions of Spherical Polar Coordinates

This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.     

A new supersymmetric classical Boussinesq equation

In this paper, we obtain a supersymmetric generalization for the classical Boussinesq equation. We show that the supersymmetric equation system passes the Painlev\'{e test and we also calculate its one- and two-soliton solutions.     

A new supersymmetric classical Boussinesq equation

In this paper, we obtain a supersymmetric generalization for the classical Boussinesq equation. We show that the supersymmetric equation system passes the Painlev\'{e test and we also calculate its one- and two-soliton solutions.