Modern Physics Letters A, ISSN 0217-7323, 08/2019, Volume 34, Issue 24, p. 1950195

Analytical solutions of the Schrödinger equation with a singular, fractional-power potential, referred to as the second Exton potential, are derived and...

integrable potentials | Stationary Schrödinger equation | energy spectrum | biconfluent Heun equation | Hermite function | EXACTLY SOLUBLE CLASS | QUANTUM | ASTRONOMY & ASTROPHYSICS | Stationary Schrodinger equation | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

integrable potentials | Stationary Schrödinger equation | energy spectrum | biconfluent Heun equation | Hermite function | EXACTLY SOLUBLE CLASS | QUANTUM | ASTRONOMY & ASTROPHYSICS | Stationary Schrodinger equation | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 07/2019, Volume 127, pp. 89 - 120

In this paper, we prove that the spectral curve Γn of the generalized Lamé equation with the Treibich–Verdier...

Spectral curve | Degree of the addition map | Generalized Lamé equation | SYSTEM | MATHEMATICS, APPLIED | Generalized Lame equation | PROPERTY | COVERS | MEAN-FIELD EQUATIONS | POTENTIALS | MATHEMATICS | PAINLEVE VI EQUATION | HEUN EQUATION | ANSATZ

Spectral curve | Degree of the addition map | Generalized Lamé equation | SYSTEM | MATHEMATICS, APPLIED | Generalized Lame equation | PROPERTY | COVERS | MEAN-FIELD EQUATIONS | POTENTIALS | MATHEMATICS | PAINLEVE VI EQUATION | HEUN EQUATION | ANSATZ

Journal Article

Journal of Sound and Vibration, ISSN 0022-460X, 03/2020, Volume 469, p. 115169

This paper aims at presenting closed-form general analytical solutions of the Webster equation describing plane elastic or acoustic waves. The considered...

Horn | Webster equation | Triconfluent Heun equation | Triconfluent Heun function | Non-uniform cross-sectioned waveguide | ACOUSTICS | MECHANICS | FREE LONGITUDINAL VIBRATION | HORN EQUATION | RODS | ENGINEERING, MECHANICAL | Nonlinear equations | Ducts | Resonant frequencies | Approximations | Exact solutions | Acoustics | Mathematical functions | Polynomials | Acoustic waves

Horn | Webster equation | Triconfluent Heun equation | Triconfluent Heun function | Non-uniform cross-sectioned waveguide | ACOUSTICS | MECHANICS | FREE LONGITUDINAL VIBRATION | HORN EQUATION | RODS | ENGINEERING, MECHANICAL | Nonlinear equations | Ducts | Resonant frequencies | Approximations | Exact solutions | Acoustics | Mathematical functions | Polynomials | Acoustic waves

Journal Article

Chemical Physics Letters, ISSN 0009-2614, 05/2017, Volume 676, pp. 169 - 173

[Display omitted] •We construct a double-well potential for which the Schrödinger equation can be exactly solved.•The wave function is expressed via the...

Confluent Heun’s function | Schrödinger equation | Hydrogen bond | Confluent Heun's function | CHEMISTRY, PHYSICAL | Schrodinger equation | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MOLECULES | Hydrogen | Hydrogen bonding | Bonds | Analysis

Confluent Heun’s function | Schrödinger equation | Hydrogen bond | Confluent Heun's function | CHEMISTRY, PHYSICAL | Schrodinger equation | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | MOLECULES | Hydrogen | Hydrogen bonding | Bonds | Analysis

Journal Article

Nelineinaya Dinamika, ISSN 1816-448X, 2019, Volume 15, Issue 1, pp. 79 - 85

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2018, Volume 59, Issue 2, p. 22105

We present a definition of integrability for the one-dimensional Schrödinger equation, which encompasses all known integrable systems, i.e., systems for which...

PHYSICS, MATHEMATICAL | HEUN | Mathematical Physics | Mathematics

PHYSICS, MATHEMATICAL | HEUN | Mathematical Physics | Mathematics

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2009, Volume 263, Issue 1, pp. 149 - 194

Several results including integral representation of solutions and Hermite-Krichever Ansatz on Heun's equation are generalized to a certain class of Fuchsian...

SYSTEM | MATHEMATICS | SCHLESINGER EQUATIONS | COVERS | HEUN EQUATION

SYSTEM | MATHEMATICS | SCHLESINGER EQUATIONS | COVERS | HEUN EQUATION

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 338, pp. 624 - 630

We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these...

Confluent hypergeometric function | Bessel function | Confluent Heun equation | Recurrence relation | 02.30.Gp Special functions | 02.30.Hq Ordinary differential equations | 02.30.Mv Approximations and expansions | MATHEMATICS, APPLIED | TERMS

Confluent hypergeometric function | Bessel function | Confluent Heun equation | Recurrence relation | 02.30.Gp Special functions | 02.30.Hq Ordinary differential equations | 02.30.Mv Approximations and expansions | MATHEMATICS, APPLIED | TERMS

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 02/2014, Volume 31, Issue 4, p. 45003

This work deals with the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on massive scalar fields....

Kerr-Newman metric | Heun's differential equations | Klein-Gordon equation | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Charging | Mathematical analysis | Exact solutions | Scalars | Black holes (astronomy) | Rotating | Quantum gravity | Physics - General Relativity and Quantum Cosmology

Kerr-Newman metric | Heun's differential equations | Klein-Gordon equation | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Charging | Mathematical analysis | Exact solutions | Scalars | Black holes (astronomy) | Rotating | Quantum gravity | Physics - General Relativity and Quantum Cosmology

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 3/2018, Volume 57, Issue 3, pp. 652 - 663

For the spatially open Friedmann–Robertson–Walker (FRW) Universe with stiff matter and radiation as non-interacting matter sources, the scale function coming...

Quantum cosmology | Heun functions | Theoretical, Mathematical and Computational Physics | Quantum Physics | Friedmann equation | Physics, general | Physics | Elementary Particles, Quantum Field Theory | COSMOLOGY | SCALAR FIELD | PHYSICS, MULTIDISCIPLINARY | Toiletries industry | Radiation

Quantum cosmology | Heun functions | Theoretical, Mathematical and Computational Physics | Quantum Physics | Friedmann equation | Physics, general | Physics | Elementary Particles, Quantum Field Theory | COSMOLOGY | SCALAR FIELD | PHYSICS, MULTIDISCIPLINARY | Toiletries industry | Radiation

Journal Article

Constructive Approximation, ISSN 0176-4276, 2014, Volume 39, Issue 1, pp. 75 - 83

Painleve equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas...

Heun deformed equation | Apparent singularity | Painlevé equation | 2×2 Fuchsian linear system | Heun equation | Euler integral transform | Antiquantization

Heun deformed equation | Apparent singularity | Painlevé equation | 2×2 Fuchsian linear system | Heun equation | Euler integral transform | Antiquantization

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2019, Volume 132, pp. 251 - 272

In this paper, the second in a series, we continue to study the generalized Lamé equation with the Treibich-Verdier...

Mean field equation | Generalized Lamé equation | Pre-modular form | MATHEMATICS | MATHEMATICS, APPLIED | Generalized Lame equation | MEAN-FIELD EQUATIONS | POTENTIALS | HEUN EQUATION

Mean field equation | Generalized Lamé equation | Pre-modular form | MATHEMATICS | MATHEMATICS, APPLIED | Generalized Lame equation | MEAN-FIELD EQUATIONS | POTENTIALS | HEUN EQUATION

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 10/2016, Volume 33, Issue 22, p. 225011

Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in...

STELLAR ORBITS | QUANTUM SCIENCE & TECHNOLOGY | Klein-Gordon-Fock equation | PARTICLES | PHYSICS, MULTIDISCIPLINARY | Heun functions | FIELD | CONNECTION PROBLEM | fuchsian differential equations | DE-SITTER | Kerr-Newman-(anti) de Sitter black hole | ASTRONOMY & ASTROPHYSICS | cosmological constant | inverse problems | MASS | GALACTIC-CENTER | EQUATORIAL PHOTON MOTION | PHYSICS, PARTICLES & FIELDS

STELLAR ORBITS | QUANTUM SCIENCE & TECHNOLOGY | Klein-Gordon-Fock equation | PARTICLES | PHYSICS, MULTIDISCIPLINARY | Heun functions | FIELD | CONNECTION PROBLEM | fuchsian differential equations | DE-SITTER | Kerr-Newman-(anti) de Sitter black hole | ASTRONOMY & ASTROPHYSICS | cosmological constant | inverse problems | MASS | GALACTIC-CENTER | EQUATORIAL PHOTON MOTION | PHYSICS, PARTICLES & FIELDS

Journal Article

Theoretical and Mathematical Physics(Russian Federation), ISSN 0040-5779, 04/2018, Volume 195, Issue 1, pp. 494 - 512

We derive the most general families of first- and second-order differential operators semicommuting with the Heun class differential operators. Among these...

confluent Heun equation | commuting operator | triconfluent Heun equation | semicommuting operator | Heun equation | factorization | double confluent Heun equation | biconfluent Heun equation | generalized Heun equation | PHYSICS, MULTIDISCIPLINARY | CONNECTION PROBLEM | EQUATIONS | PHYSICS, MATHEMATICAL | BLACK-HOLES | CHARGED-PARTICLES | Family | Differential equations

confluent Heun equation | commuting operator | triconfluent Heun equation | semicommuting operator | Heun equation | factorization | double confluent Heun equation | biconfluent Heun equation | generalized Heun equation | PHYSICS, MULTIDISCIPLINARY | CONNECTION PROBLEM | EQUATIONS | PHYSICS, MATHEMATICAL | BLACK-HOLES | CHARGED-PARTICLES | Family | Differential equations

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2018, Volume 14

We describe the close connection between the linear system for the sixth Painleve equation and the general Heun equation, formulate the Riemann-Hilbert problem...

Heun polynomials | Painlevé equations | Riemann-Hilbert problem | Painleve equations | MONODROMY | TRANSCENDENTS | PHYSICS, MATHEMATICAL | PAINLEVE | DEFORMATION | ORDINARY DIFFERENTIAL-EQUATIONS | Mathematical analysis

Heun polynomials | Painlevé equations | Riemann-Hilbert problem | Painleve equations | MONODROMY | TRANSCENDENTS | PHYSICS, MATHEMATICAL | PAINLEVE | DEFORMATION | ORDINARY DIFFERENTIAL-EQUATIONS | Mathematical analysis

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 07/2018, Volume 14

The q-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these...

Degeneration | Quasi-Exact solvability | Regular singularity | Heun equation | Q-Deformation | MODELS | regular singularity | quasi-exact solvability | DIFFERENCE-OPERATORS | PHYSICS, MATHEMATICAL | q-deformation | degeneration | Singularities | Subspaces | Deformation

Degeneration | Quasi-Exact solvability | Regular singularity | Heun equation | Q-Deformation | MODELS | regular singularity | quasi-exact solvability | DIFFERENCE-OPERATORS | PHYSICS, MATHEMATICAL | q-deformation | degeneration | Singularities | Subspaces | Deformation

Journal Article

Modern Physics Letters A, ISSN 0217-7323, 05/2018, Volume 33, Issue 16, p. 1850090

We study the wave equation governing massless fields of all spins (s = 0, 1 2 , 1, 3 2 and 2) in the most general spherical symmetric metric of conformal...

Wave equation | conformal gravity | Heun equation | PERTURBATIONS | QUASI-NORMAL MODES | STABILITY | FIELD | PHYSICS, NUCLEAR | HARMONICS | PHYSICS, MATHEMATICAL | BLACK-HOLES | ASTRONOMY & ASTROPHYSICS | KERR-DE-SITTER | PHYSICS, PARTICLES & FIELDS

Wave equation | conformal gravity | Heun equation | PERTURBATIONS | QUASI-NORMAL MODES | STABILITY | FIELD | PHYSICS, NUCLEAR | HARMONICS | PHYSICS, MATHEMATICAL | BLACK-HOLES | ASTRONOMY & ASTROPHYSICS | KERR-DE-SITTER | PHYSICS, PARTICLES & FIELDS

Journal Article

ASTROPHYSICS AND SPACE SCIENCE, ISSN 0004-640X, 06/2015, Volume 357, Issue 2, pp. 1 - 5

The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We...

Spin fields | BACKGROUNDS | Heun's equation | PERTURBATIONS | GENERAL-RELATIVITY | Black holes | STABILITY | ASTRONOMY & ASTROPHYSICS | HARMONICS | KERR-DE-SITTER | BLACK-HOLES | Electromagnetism | Studies | Cosmology | Astrophysics | Cosmological constant | Gravitation | Propagation | Mathematical analysis | Neutrinos | Scalars | Black holes (astronomy) | Event horizon

Spin fields | BACKGROUNDS | Heun's equation | PERTURBATIONS | GENERAL-RELATIVITY | Black holes | STABILITY | ASTRONOMY & ASTROPHYSICS | HARMONICS | KERR-DE-SITTER | BLACK-HOLES | Electromagnetism | Studies | Cosmology | Astrophysics | Cosmological constant | Gravitation | Propagation | Mathematical analysis | Neutrinos | Scalars | Black holes (astronomy) | Event horizon

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 09/2016, Volume 106, Issue 3, pp. 546 - 581

In literature, it is known that any solution of Painlevé VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on CP1. In...

Isomonodromy theory | Hamiltonian system | The elliptic form | Painlevé VI equation | MATHEMATICS | MONODROMY | MATHEMATICS, APPLIED | 2ND-ORDER | Painleve VI equation | DIFFERENTIAL-EQUATIONS | HEUN EQUATION | DEFORMATION

Isomonodromy theory | Hamiltonian system | The elliptic form | Painlevé VI equation | MATHEMATICS | MONODROMY | MATHEMATICS, APPLIED | 2ND-ORDER | Painleve VI equation | DIFFERENTIAL-EQUATIONS | HEUN EQUATION | DEFORMATION

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 5/2014, Volume 179, Issue 2, pp. 543 - 549

Euler integral symmetries relate solutions of ordinary linear differential equations and generate integral representations of the solutions in several cases or...

apparent singularity | confluent Heun equation | Theoretical, Mathematical and Computational Physics | monodromy | Applications of Mathematics | Physics | Euler integral transform | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

apparent singularity | confluent Heun equation | Theoretical, Mathematical and Computational Physics | monodromy | Applications of Mathematics | Physics | Euler integral transform | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

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