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Communications in Theoretical Physics 2008年第8期50卷 335-340页

作者： JIA Wen-Zhi WANG Shun-Jin Center of Theoretical Physics Department of Physics Sichuan University Chengdu 610064 China Center of Theoretical Nuclear Physics National Laboratory of Heavy Ion Accelerator Lanzhou 730000 China

We find that in a supersymmetric quantum mechanics （SUSY QM） system, in addition to supersymmetric algebra, an associated SU（2） algebra can be obtained by using semiunitary （SUT） operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ（2） SUσ（2） symmetry in the context of the relativistic Pauli Hamilt onian squared. We show that there exists also an SU（2） symmetry associated with the supersvmmetrv of the Dirac particle.

关键词： supersymmetric quantum mechanics Dirac equation semi-unitary transformation

Generating of Conditionally Exactly Soluble Potentials by Method of supersymmetric quantum mechanics

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Communications in Theoretical Physics 2007年第2期47卷 225-228页

作者： QIAN Shang-Wu MIAO Chun-Hui GU Zhi-Yu Physics Department Peking University Beijing 100871 China Physics Department Capital Normal University Beijing 100037 China

This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate v... 详细信息

关键词： supersymmetric quantum mechanics conditionally exactly soluble potential SWKB approximation variational method energy level

Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

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Chinese Physics B 2011年第12期20卷 52-56页

作者：桑明煌余子星李翠翠涂凯 Department of Physics Jiangxi Normal University

For the conventional translational shape-invariant potentials （TSIPs）, it has demonstrated that the phase contribution devoted by the scattered subwaves in the analytical transfer matrix quantization condition is integrable and independent of n. Based on this fact we propose a novel strategy to generate the whole set of conventional TSIPs and classify them into three types. The generating functions are given explicitly and the Morse potential is taken as an example to illustrate this strategy.

关键词： translational shape-invariant potentials supersymmetric quantum mechanics analyticaltransfer matrix method scattered subwaves generating function

Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

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Chinese Physics B 2012年第4期21卷 106-116页

作者：孙越田贵花董锟 School of Science Beijing University of Posts And TelecommunicationsBeijing 100876China

By using the super-symmetric quantum mechanics （SUSYQM） method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W0 to W4 the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.

关键词： spheroidal wave equation supersymmetric quantum mechanics super-potential eigen-value and eigenfunetion

Verification of the spin-weighted spheroidal equation in the case of s=1

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Chinese Physics B 2012年第4期21卷 117-125页

作者：张晴田贵花孙越董锟 School of Sciences Beijing University of Posts and TelecommunicationsBeijing 100876China

The spin-weighted spheroidal equation in the case of s = 1 is studied. By transforming the independent variables, we make it take the Schr6dinger-like form. This Schr6dinger-like equation is very interesting in itself. We investigate it by using super-symmetric quantum mechanics and obtain the ground eigenvalue and eigenfunction, which are consistent with the results previously obtained.

关键词： spheroidal wave equation supersymmetric quantum mechanics super-potential eigen- value and eigenfunction

Transmission time in the reflectionless complex potential

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Chinese Physics B 2014年第10期23卷 7-11页

作者：殷澄王贤平单鸣雷韩庆邦朱昌平 Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology Hohai University School of Physics and Communication Electronics Jiangxi Normal University

A phase time definition directly obtained from the Schr6dinger equation is used to investigate the time delay of a particle scattered by complex reflectionless potential. The artifacts introduced by truncating in the numerical simulation are clarified. The time delay of the transmitted wave packet is found to be equal to the reflection time of the truncated potential. Both time delays are the same as the traversal time in the free space, but shorter than the time taken by a classical particle to pass the same potential.

关键词： complex reflectionless potentials transmission time supersymmetric quantum mechanics

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

Spin-weighted spheroidal equation in the case of s=1

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Chinese Physics B 2011年第6期20卷 150-159页

作者：孙越田贵花董锟 School of Science Beijing University of Posts and Telecommunications

We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of supersymmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s ： 1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigenfunctions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.

关键词： spheroidal wave equation supersymmetric quantum mechanics super-potential eigenvalue and eigenfunction

Approximate Solution of D-Dimensional Klein-Gordon Equation with Hulthn-Type Potential via SUSYQM

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Communications in Theoretical Physics 2011年第9期56卷 423-428页

作者： H.Hassanabadi S.Zarrinkamar H.Rahimov Physics Department Shahrood University of TechnologyShahroodIran P.O.Box ***-316 ShahroodIran Department of Basic Sciences Garmsar BranchIslamic Azad University Computer Engineering Department Shahrood University of Technology

Approximate analytical solutions of the D-dimensional Klein-Gordon equation are obtained for the scalarand vector general Hulthen-type potential and position-dependent mass with any l by using the concept of supersymm... 详细信息

关键词： Klein-Gordon equation D-dimensional space supersymmetric quantum mechanics

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