A Novel Exact Solution of the 2+1-Dimensional Radial Dirac Equation for the Generalized Dirac Oscillator with the Inverse Potentials

The generalized Dirac oscillator as one of the exact solvable models in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse cubic, quartic, quintic, and sixth power potentials in radial Dirac equation were further given by means of the Bethe ansatz method. And finally, the corresponding exact solutions in this paper were further discussed.

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DIRAC OSCILLATORS AND QUASI-EXACTLY SOLVABLE OPERATORS

Modern Physics Letters A ◽

10.1142/s0217732305018128 ◽

2005 ◽

Vol 20 (25) ◽

pp. 1875-1885 ◽

Cited By ~ 8

Author(s):

Y. BRIHAYE ◽

A. NININAHAZWE

Keyword(s):

Dirac Equation ◽

Dirac Operator ◽

Spherically Symmetric ◽

Dirac Oscillator ◽

Generic Polynomial ◽

Exactly Solvable ◽

Spectral Equation ◽

Radial Variable ◽

Radial Dirac Equation

The Dirac equation is formulated in the background of three types of physically relevant potentials: scalar, vector and "Dirac-oscillator" potentials. Assuming these potentials to be spherically-symmetric and with generic polynomial forms in the radial variable, we construct the corresponding radial Dirac equation. Cases where this linear spectral equation is exactly solvable or quasi-exactly solvable are worked out in details. When available, relations between the radial Dirac operator and some super-algebra are pointed out.

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Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials

Advances in High Energy Physics ◽

10.1155/2018/1940925 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9

Author(s):

Zahra Bakhshi

Keyword(s):

Quantum Mechanics ◽

Energy Spectrum ◽

Dirac Equation ◽

Bound States ◽

Scalar Potential ◽

Solvable Models ◽

Nonrelativistic Quantum ◽

Physical Conditions ◽

Basic Model ◽

Nonrelativistic Quantum Mechanics

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrödinger-like equation obtained by Dirac equation with the nonrelativistic solvable models is the most efficient method. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped Oscillator Potentials are accessible, when the scalar potential is equal to the vector potential. Using solvable nonrelativistic quantum mechanics systems as a basic model and considering the physical conditions provide the changes in the restrictions of relativistic parameters based on the nonrelativistic definitions of parameters.

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Dirac Equation on the Torus and Rationally Extended Trigonometric Potentials within Supersymmetric QM

Advances in High Energy Physics ◽

10.1155/2018/6891402 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Özlem Yeşiltaş

Keyword(s):

Quantum Mechanics ◽

Dirac Equation ◽

Exact Solutions ◽

Casimir Operator ◽

Supersymmetric Quantum Mechanics ◽

Algebraic Approaches

The exact solutions of the (2+1)-dimensional Dirac equation on the torus and the new extension and generalization of the trigonometric Pöschl-Teller potential families in terms of the torus parameters are obtained. Supersymmetric quantum mechanics techniques are used to get the extended potentials when the inner and outer radii of the torus are both equal and inequal. In addition, using the aspects of the Lie algebraic approaches, the iso(2,1) algebra is also applied to the system where we have arrived at the spectrum solutions of the extended potentials using the Casimir operator that matches with the results of the exact solutions.

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DIRAC EQUATION FOR A COULOMB SCALAR, VECTOR AND TENSOR INTERACTION

International Journal of Modern Physics A ◽

10.1142/s0217751x11051287 ◽

2011 ◽

Vol 26 (06) ◽

pp. 1011-1018 ◽

Cited By ~ 18

Author(s):

S. ZARRINKAMAR ◽

H. HASSANABADI ◽

A. A. RAJABI

Keyword(s):

Quantum Mechanics ◽

Dirac Equation ◽

Exact Solutions ◽

Pseudospin Symmetry ◽

Spin Symmetry ◽

Tensor Interaction ◽

Wave Functions ◽

Energy Eigenvalues ◽

Coulomb Term

There is now motivating experimental evidence for relativistic symmetries in nuclei and hadrons, namely pseudospin and spin symmetry limits of the Dirac equation besides the old theoretical backgrounds. The most fundamental ingredients in such studies are definitely the wave functions and energy eigenvalues. Here, having in mind the importance of the Coulomb term as well as the degeneracy-removing role of tensor interaction, we obtain the exact solutions to the problem for Coulomb scalar, vector and tensor terms in both spin and pseudospin symmetry limits. We see that, contrary to many other common cumbersome techniques, the problem is simply solved via the methodology of supersymmetric quantum mechanics.

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Discussion on Exact Solution of Dirac Equation with Generalized Exponential Potential in the Presence of Generalized Uncertainty Principle

Few-Body Systems ◽

10.1007/s00601-021-01643-y ◽

2021 ◽

Vol 62 (3) ◽

Author(s):

Zi-Long Zhao ◽

Hao Wu ◽

Zheng-Wen Long

Keyword(s):

Exact Solution ◽

Dirac Equation ◽

Uncertainty Principle ◽

Generalized Uncertainty Principle ◽

Exponential Potential

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An inhomogeneous problem for an elastic half-strip: An exact solution

Mathematics and Mechanics of Solids ◽

10.1177/1081286521996418 ◽

2021 ◽

pp. 108128652199641

Author(s):

Mikhail D Kovalenko ◽

Irina V Menshova ◽

Alexander P Kerzhaev ◽

Guangming Yu

Keyword(s):

Exact Solution ◽

Boundary Conditions ◽

Exact Solutions ◽

Boundary Value Problems ◽

Boundary Value ◽

Theory Of Elasticity ◽

Orthogonality Relation ◽

Infinite Strip ◽

Inhomogeneous Problem ◽

Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

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Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

Journal of Applied Analysis ◽

10.1515/jaa-2020-2031 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Riccardo Cristoferi

Keyword(s):

Exact Solution ◽

Exact Solutions ◽

Total Variation ◽

Piecewise Constant ◽

Geometrical Properties ◽

Total Variation Denoising ◽

Fidelity Term ◽

Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

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