Exact solution of the curved Dirac equation in polar coordinates: master function approach (Q889063): Difference between revisions

The Dirac equation for a charged particle in (2+1) dimensions is studied. Using shape-invariant potentials, it is exactly solved for some particular electromagnetic fields.

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reviewed by

Mohammad Khorrami

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zbMATH Keywords

Dirac equation

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shape-invariant potentials

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.1155/2015/612757

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cites work

Approximate solutions of the Dirac equation for the Rosen–Morse potential including the spin-orbit centrifugal term

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Generalized nuclear Woods-Saxon potential under relativistic spin symmetry limit

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Dirac equation for generalized Pöschl-Teller scalar and vector potentials and a Coulomb tensor interaction by Nikiforov-Uvarov method

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Exact solution of the Dirac equation for the Yukawa potential with scalar and vector potentials and tensor interaction

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Exact solutions of Dirac equation on a 2D gravitational background

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Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field

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Dirac equation in some homogeneous space-times, separation of variables and exact solutions

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Exact solution of Dirac equation in 2+1 dimensional gravity

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Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of non-central electromagnetic potentials

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Separation of variables and exact solution of the Klein–Gordon and Dirac equations in an open universe

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Bound states of the Dirac equation with vector and scalar Eckart potentials

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Bound states of relativistic particles in the generalized symmetrical double-well potential

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Bound states of the Dirac equation for the $PT$-symmetric generalized Hulthén potential by the Nikiforov-Uvarov method

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Approximate arbitrary-state solutions of Dirac equation for modified deformed Hylleraas and modified Eckart potentials by the NU method

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Dynamical breaking of supersymmetry

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Derivation of the exact spectra of the Schrödinger equation by means of supersymmetry

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Parasupersymmetry and shape invariance in differential equations of mathematical physics and quantum mechanics

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Another bunch of superpotentials in terms of a master function

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Dirac equation for a spin-$frac12$ charged particle on the 2D sphere S2 and the hyperbolic plane H2

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Solution of the Dirac equation on the homogeneous manifoldSL(2,c)/GL(1,c) in the presence of a magnetic monopole field

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Exact solution of the Dirac equation for a spin-$\frac 12$ charged particle in two-dimensional and three-dimensional Euclidean spaces with shape invariance symmetry

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Q4001777

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Relativistic extension of shape-invariant potentials

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Solution of the Dirac equation with position-dependent mass in the Coulomb field

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The $(2+1)$ curved Dirac equation in polar coordinates in the presence of electromagnetic field

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Q4440310

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A search for shape-invariant solvable potentials

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Identifiers

zbMATH Open document ID

1436.81034

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DOI

10.1155/2015/612757

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:889063

@@ description / en / description / en @@
-scientific article
+scientific article; zbMATH DE number 6505155
@@ Property / MaRDI profile type @@
+Publication
@@ Property / MaRDI profile type: Publication / rank @@
+Normal rank
@@ Property / full work available at URL @@
+https://doi.org/10.1155/2015/612757
+Normal rank
@@ Property / OpenAlex ID @@
+W1589798718
@@ Property / OpenAlex ID: W1589798718 / rank @@
+Normal rank
@@ Property / cites work @@
+Approximate solutions of the Dirac equation for the Rosen–Morse potential including the spin-orbit centrifugal term
+Normal rank
@@ Property / cites work @@
+Generalized nuclear Woods-Saxon potential under relativistic spin symmetry limit
+Normal rank
@@ Property / cites work @@
+Dirac equation for generalized Pöschl-Teller scalar and vector potentials and a Coulomb tensor interaction by Nikiforov-Uvarov method
+Normal rank
@@ Property / cites work @@
+Exact solution of the Dirac equation for the Yukawa potential with scalar and vector potentials and tensor interaction
+Normal rank
@@ Property / cites work @@
+Exact solutions of Dirac equation on a 2D gravitational background
+Normal rank
@@ Property / cites work @@
+Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field
+Normal rank
@@ Property / cites work @@
+Dirac equation in some homogeneous space-times, separation of variables and exact solutions
+Normal rank
@@ Property / cites work @@
+Exact solution of Dirac equation in 2+1 dimensional gravity
+Normal rank
@@ Property / cites work @@
+Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of non-central electromagnetic potentials
+Normal rank
@@ Property / cites work @@
+Separation of variables and exact solution of the Klein–Gordon and Dirac equations in an open universe
+Normal rank
@@ Property / cites work @@
+Bound states of the Dirac equation with vector and scalar Eckart potentials
+Normal rank
@@ Property / cites work @@
+Bound states of relativistic particles in the generalized symmetrical double-well potential
+Normal rank
@@ Property / cites work @@
+Bound states of the Dirac equation for the \(PT\)-symmetric generalized Hulthén potential by the Nikiforov-Uvarov method
+Normal rank
@@ Property / cites work @@
+Approximate arbitrary-state solutions of Dirac equation for modified deformed Hylleraas and modified Eckart potentials by the NU method
+Normal rank
@@ Property / cites work @@
+Dynamical breaking of supersymmetry
@@ Property / cites work: Dynamical breaking of supersymmetry / rank @@
+Normal rank
@@ Property / cites work @@
+Derivation of the exact spectra of the Schrödinger equation by means of supersymmetry
+Normal rank
@@ Property / cites work @@
+Parasupersymmetry and shape invariance in differential equations of mathematical physics and quantum mechanics
+Normal rank
@@ Property / cites work @@
+Another bunch of superpotentials in terms of a master function
+Normal rank
@@ Property / cites work @@
+Dirac equation for a spin-$frac12$ charged particle on the 2D sphere S2 and the hyperbolic plane H2
+Normal rank
@@ Property / cites work @@
+Solution of the Dirac equation on the homogeneous manifold<i>SL</i>(2,<i>c</i>)/<i>GL</i>(1,<i>c</i>) in the presence of a magnetic monopole field
+Normal rank
@@ Property / cites work @@
+Exact solution of the Dirac equation for a spin-\(\frac 12\) charged particle in two-dimensional and three-dimensional Euclidean spaces with shape invariance symmetry
+Normal rank
@@ Property / cites work @@
+Q4001777
@@ Property / cites work: Q4001777 / rank @@
+Normal rank
@@ Property / cites work @@
+Relativistic extension of shape-invariant potentials
+Normal rank
@@ Property / cites work @@
+Solution of the Dirac equation with position-dependent mass in the Coulomb field
+Normal rank
@@ Property / cites work @@
+The \((2+1)\) curved Dirac equation in polar coordinates in the presence of electromagnetic field
+Normal rank
@@ Property / cites work @@
+Q4440310
@@ Property / cites work: Q4440310 / rank @@
+Normal rank
@@ Property / cites work @@
+A search for shape-invariant solvable potentials
@@ Property / cites work: A search for shape-invariant solvable potentials / rank @@
+Normal rank
@@ links / mardi / name / links / mardi / name @@
+Publication:889063