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Exact Solution of Klein-Gordon Equation for Charged Particle in Magnetic Field with shape Invariant Method

Communications in Theoretical Physics 2009年第6期51卷 1000-1002页

作者： M.R. Setare O. Hatami Department of Science University of Kurdistan Pasdaran Ave. Sanandaj Iran

Based on the shape invariance property we obtain exact solutions of the three-dimensional relativistic Klein Gordon equation for a charged particle moving in the presence of a certain varying magnetic field, and we al... 详细信息

关键词： Klein Gordon equation shape invariance supersymmetric quantum mechanics exact solutions magnetic field

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Solving the spin-weighted spheroidal wave equation

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Chinese Physics B 2013年第6期22卷 110-114页

作者：李玉祯田贵花董锟 School of Sciences Beijing University of Posts and Telecommunications

In this paper we solve spin-weighted spheroidal wave equations through super-symmetric quantum mechanics with a different expression of the super-potential. We use the shape invariance property to compute the ＂excited＂ eigenvalues and eigenfunctions. The results are beneficial to researchers for understanding the properties of the spin-weighted spheroidal wave more deeply, especially its integrability.

关键词： spin-weighted spherical wave equation supersymmetric quantum mechanics shape invariance recurrence relation

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Six—Parameter Exponential—Type Potential and the Identity for the Exponential—Type Potentials

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Communications in Theoretical Physics 2002年第5期37卷 523-530页

作者： JIAChun－Sheng ZENGXiang－Lin 等 StateKeyLaboratoryofOilandGasReservoirGeologyandExploitation SouthwestPetroleumInstituteNanchong637001SichuanProvinceChina GraduateSchool SouthwestPetroleumInstituteNanchong6370

We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained byusing the supersymmetric shape invariance technique. Choosing appropriate parameters, four classes of exponential-typepotentials and their exact energy spectra are reduced from the SPEP and a general energy level formula, *** class shows the identity except for the different definitions of parameters.

关键词： six-parameter exponential-type potential shape invariance energy eigenvalue

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Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

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Chinese Physics B 2011年第7期20卷 123-132页

作者：董锟田贵花孙越 School of Science Beijing University of Posts and Telecommunications

The spin-weighted spheroidal equation in the case of s = 1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics. The first-five terms of the superpotential in the series of parameter β are given. The general form for the n-th term of the superpotential is also obtained, which could also be derived from the previous terms Wk, k 〈 n. From these results, it is easy to obtain the ground eigenfunction of the equation. Furthermore, the shape-invariance property in the series of parameter β is investigated and is proven to be kept. This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics. We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.

关键词： spheroidal wave equation supersymmetric quantum mechanics superpotential shape invariance

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Bound states of the Klein-Gordon and Dirac equation for scalar and vector pseudoharmonic oscillator potentials

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Chinese Physics B 2004年第3期13卷 279-282页

作者：陈刚陈子栋楼智美陈刚陈子栋楼智美 DepartmentofPhysics ShaoxingCollegeofArtsandSciencesShaoxing312000China

The exact bound state solutions of the Klein-Gordon equation and Dirac equation with scalar and vector pseudoharmonic oscillator potentials are obtained in this paper. Furthermore, we have used the supersymmetric quan... 详细信息

关键词： pseudoharmonic oscillator potential Klein-Gordon equation Dirac equation bound state supersymmetric quantum mechanics shape invariance

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A New Class of Exactly Solvable Models within the Schrodinger Equation with Position Dependent Mass

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Journal of Applied Mathematics and Physics 2019年第5期7卷 1013-1026页

作者： Anis Dhahbi Yassine Chargui Adel Trablesi Physics Department College of Science and Arts at ArRass Qassim University Al-Mulida KSA Universite de Tunis El Manar Faculte des Sciences de Tunis Unite de Recherche de Physique Nucleaire et des Hautes Energies Tunis Tunisie

The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.

关键词： Schrodinger Equation Position Dependent Mass Kinetic Energy Operator Solvable Models Supersymmetric Quantum Mechanics shape invariance

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