One-dimensional quasi-exactly solvable Schrödinger equations (Q521772)

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English	One-dimensional quasi-exactly solvable Schrödinger equations	scientific article

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scholarly article

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One-dimensional quasi-exactly solvable Schrödinger equations (English)

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Physics Reports

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publication date

12 April 2017

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full work available at URL

https://arxiv.org/abs/1603.02992

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Alexander~V. Turbiner

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MaRDI profile type

MaRDI publication profile

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Spectral Riemann surfaces of the Sturm-Liouville operator and quasiexactly solvable problems

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Quasi-exactly-solvable problems and sl(2) algebra

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Quantal problems with partial algebraization of the spectrum

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QUASI-EXACTLY-SOLVABLE QUANTAL PROBLEMS: ONE-DIMENSIONAL ANALOGUE OF RATIONAL CONFORMAL FIELD THEORIES

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CONTINUOUS SUGAWARA-LIKE REALIZATION OF c=1 CONFORMAL MODELS

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ON AFFINE VIRASORO CONSTRUCTIONS FOR <font>SL</font>(2,ℝ) CURRENT ALGEBRA

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Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories.

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On a ''universal'' class of WZW-type conformal models

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Irrational conformal field theory

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Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem

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On solvability and integrability of the Rabi model

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On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations

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Lie-algebras and linear operators with invariant subspaces

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Invariant identities in the Heisenberg algebra

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EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS

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Hidden algebras of the (super) Calogero and Sutherland models

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SUTHERLAND-TYPE TRIGONOMETRIC MODELS, TRIGONOMETRIC INVARIANTS AND MULTIVARIATE POLYNOMIALS III: E<sub>8</sub> CASE

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Corrigendum: Quasi-exact-solvability of the ${A}_{2}/{G}_{2}$ Elliptic model: algebraic forms, ${sl}(3)/{g}^{(2)}$ hidden algebra, polynomial eigenfunctions, (2005 <i>J. Phys. A: Math. Theor.</i> <b>48</b> 155201)

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From quantum \(A_{N}\) (Calogero) to \(H_{4}\) (Rational) model

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From quantum \(A_{N}\) to \(E_{8}\) trigonometric model: space-of-orbits view

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Certain differential equations for Tchebycheff polynomials

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On reducing the Heun equation to the hypergeometric equation

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Duality and self-duality (Energy reflection symmetry) of quasi-exactly solvable periodic potentials

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Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions

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The Eigenvalues of Mathieu's Equation and their Branch Points

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Asymptotics of instability zones of the Hill operator with a two term potential

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Lame equation, sl(2) algebra and isospectral deformations

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Exact solutions of a new elliptic Calogero-Sutherland model

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Multiple algebraisations of an elliptic Calogero–Sutherland model

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The<i>BC</i><sub>1</sub>quantum elliptic model: algebraic forms, hidden algebra<i>sl</i>(2), polynomial eigenfunctions

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Lax representation with spectral parameter on a torus for integrable particle systems

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Quasi-exact solvability of Inozemtsev models

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Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

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Analytic continuation of eigenvalues of a quartic oscillator

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Zeros of eigenfunctions of some anharmonic oscillators

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Exact solutions of the Schrödinger equation for a class of three-dimensional isotropic anharmonic oscillators

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Quasi-exactly solvable quartic potential

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The exact calculation of long-range forces between atoms by perturbation theory

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CANONICAL DISCRETIZATION I: DISCRETE FACES OF (AN)HARMONIC OSCILLATOR

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On polynomial solutions of differential equations

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LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL EQUATIONS

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Hidden $sl_2$-algebra of finite-difference equations

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On pairs of difference operators satisfying [D, X]=Id

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The umbral calculus

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Canonical commutation relation preserving maps

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Polynomial relations in the Heisenberg algebra

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Continuous Hahn polynomials

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The Hahn and Meixner polynomials of an imaginary argument and some of their applications

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SOLVABILITY OF THE G<sub>2</sub> INTEGRABLE SYSTEM

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Solvability of the Hamiltonians related to exceptional root spaces: rational case

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Super Lax pairs and infinite symmetries in the 1/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">r</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>system

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Identifiers

zbMATH Open document ID

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10.1016/j.physrep.2016.06.002

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:521772

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