Extension of Nikiforov-Uvarov method for the solution of Heun equation

DOI10.1063/1.4922601zbMath1322.81029arXiv1504.03518OpenAlexW1962388879MaRDI QIDQ5264400

Hale Karayer, Doğan Demirhan, Fevzi Buyukkilic

Publication date: 27 July 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03518

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Perturbation theories for operators and differential equations in quantum theory (81Q15) Classical hypergeometric functions, ({}_2F_1) (33C05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Linear ordinary differential equations and systems in the complex domain (34M03) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (13)

The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes ⋮ Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation ⋮ Effects of topological defects and AB fields on the thermal properties, persistent currents and energy spectra with an exponential-type pseudoharmonic potential ⋮ Exact solutions of position-dependent mass Schrödinger equation with pseudoharmonic oscillator and its thermal properties using extended Nikiforov-Uvarov method ⋮ Exact solutions to the angular Teukolsky equation with s ≠ 0 ⋮ The search for fractional order in heavy quarkonia spectra ⋮ Bound state of heavy quarks using a general polynomial potential ⋮ About families of orthogonal polynomials satisfying Heun's differential equation ⋮ Analytical eigenstate solutions of Schrödinger equation with noncentral generalized oscillator potential by extended Nikiforov-Uvarov method ⋮ Comparing exact energy solutions of quartic eigenvalue polynomials in commutative, non-commutative and non-commutative phase frameworks for boson π− ⋮ Quantum field theory applications of Heun type functions ⋮ A new approach to solve the Schrodinger equation with an anharmonic sextic potential ⋮ Some special solutions of biconfluent and triconfluent Heun equations in elementary functions by extended Nikiforov-Uvarov method

Cites Work

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• About derivatives of Heun's functions from polynomial transformations of hypergeometric equations
• HEUN FUNCTIONS AND THEIR USES IN PHYSICS
• Physical applications of second-order linear differential equations that admit polynomial solutions
• Exact polynomial solutions of second order differential equations and their applications
• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• Polynomial Solutions of the Schrödinger Equation for the “Deformed” Hyperbolic Potentials by Nikiforov–Uvarov Method
• Practical Quantum Mechanics II
• A particular solution of Heun equation for Hulthen and Woods‐Saxon potentials
• On a solution of the Schrödinger equation with a hyperbolic double-well potential
• The Coulomb problem on a 3-sphere and Heun polynomials

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