Trends in Supersymmetric Quantum Mechanics (Q4973354)

scientific article; zbMATH DE number 7139472

Language	Label	Description	Also known as
English	Trends in Supersymmetric Quantum Mechanics	scientific article; zbMATH DE number 7139472

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instance of

scholarly article

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title

Trends in Supersymmetric Quantum Mechanics (English)

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author

David J. Fernández C.

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published in

Integrability, Supersymmetry and Coherent States

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publication date

3 December 2019

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full work available at URL

https://arxiv.org/abs/1811.06449

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zbMATH Keywords

supersymmetric quantum mechanics

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coherent states

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Painlevé equations

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Painlevé transcendents

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polynomial Heisenberg algebras

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factorization method

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exact solutions

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spectral design

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graphene

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MaRDI profile type

MaRDI publication profile

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cites work

Dynamical breaking of supersymmetry

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The Factorization Method

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Lie theory and special functions

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Q4715209

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New situation in quantum mechanics (wonderful potentials from the inverse problem)

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Q4525676

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Q2713345

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Factorization: little or great algorithm?

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Periodic potentials and supersymmetry

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The Script C operator in Script PScript T-symmetric quantum theories

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Inverse scattering with supersymmetric quantum mechanics

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Nonlinear supersymmetry for spectral design in quantum mechanics

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Factorization method in quantum mechanics

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Nonlinear supersymmetric quantum mechanics: concepts and realizations

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Single- and coupled-channel radial inverse scattering with supersymmetric transformations

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Q5776839

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Q5845868

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On a New Treatment of Some Eigenvalue Problems

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The Factorization Method, Hydrogen Intensities, and Related Problems

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Factorization method and new potentials with the oscillator spectrum

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Symmetries and supersymmetries of the quantum harmonic oscillator

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A general class of (essentially) iso-spectral perturbations

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Exact solutions for nonpolynomial potentials in N-space dimensions using a factorization method and supersymmetry

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Conditionally exactly solvable problems and nonlinear algebras.

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Factorization method and singular Hamiltonians

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\(C_ \lambda\)-extended harmonic oscillator and (para)supersymmetric quantum mechanics.

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Q4256771

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Isospectral problem for Schrödinger operator: Evolutional viewpoint

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GENERATING COMPLEX POTENTIALS WITH REAL EIGENVALUES IN SUPERSYMMETRIC QUANTUM MECHANICS

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FRACTIONAL SUPERSYMMETRIC QUANTUM MECHANICS, TOPOLOGICAL INVARIANTS AND GENERALIZED DEFORMED OSCILLATOR ALGEBRAS

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One-parameter nonrelativistic supersymmetry for microtubules

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SUSY approach to Pauli Hamiltonians with an axial symmetry

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Factorizations of one-dimensional classical systems

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The quantum brachistochrone problem for non-Hermitian Hamiltonians

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SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM

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Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanics

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SUSUSY Quantum Mechanics

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New isospectral oscillator potentials.

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A simple generation of exactly solvable anharmonic oscillators

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Quantum Mechanical Spectral Engineering by Scaling Intertwining

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Group theoretical approach to the intertwined Hamiltonians

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Group approach to the factorization of the radial oscillator equation

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Wronskian formula for confluent second-order supersymmetric quantum mechanics

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Supersymmetric partners of the trigonometric Pöschl–Teller potentials

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Higher order supersymmetric truncated oscillators

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Coherent states for isospectral oscillator Hamiltonians

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Distorted Heisenberg algebra and coherent states for isospectral oscillator Hamiltonians

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A family of complex potentials with real spectrum

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Painlevé IV coherent states

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Coherent states for Hamiltonians generated by supersymmetry

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Elementary systems with partial finite ladder spectra

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Polynomial Heisenberg algebras

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Third-order differential ladder operators and supersymmetric quantum mechanics

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Second order SUSY transformations with `complex energies'

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Gamow-Siegert functions and Darboux-deformed short range potentials

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Non-Hermitian Hamiltonians and the Painlevé IV equation with real parameters

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Complex SUSY transformations and the Painlevé IV equation

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Complex oscillator and Painlevé IV equation

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The finite difference algorithm for higher order supersymmetry

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The confluent algorithm in second-order supersymmetric quantum mechanics

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Hyperconfluent third-order supersymmetric quantum mechanics

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Wronskian differential formula for confluent supersymmetric quantum mechanics

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The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

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The generalized zero-mode supersymmetry scheme and the confluent algorithm

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On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm

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Wronskian differential formula for \(k\)-confluent SUSY QM

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Recursive representation of Wronskians in confluent supersymmetric quantum mechanics

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Second-order supersymmetric periodic potentials

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Darboux transformations for Lamé potentials.

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The phenomenon of Darboux displacements

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Nonlocal supersymmetric deformations of periodic potentials

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New supersymmetric partners for the associated Lamé potentials

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A new effective mass Hamiltonian and associated Lamé equation: bound states

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Exactly solvable associated Lamé potentials and supersymmetric transformations

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\(N\)-fold supersymmetry in quantum mechanics: general formalism

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𝒩-fold supersymmetry in quantum mechanics—analyses of particular models

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Type A \(N\)-fold supersymmetry and generalized Bender-Dunne polynomials

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A new family of \(N\)-fold supersymmetry: type B

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Existence of different intermediate Hamiltonians in type A \({\mathcal N}\)-fold supersymmetry

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Nonlinear supersymmetry: from classical to quantum mechanics

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Hidden nonlinear supersymmetry of finite-gap Lamé equation

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Self-Isospectrality, Special Supersymmetry, and their Effect on the Band Structure

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Finite-gap systems, tri-supersymmetry and self-isospectrality

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Dressing chains and the spectral theory of the Schrödinger operator

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Nonlinear chains and Painlevé equations

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Cyclic shape invariant potentials.

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Systems with higher-order shape invariance: spectral and algebraic properties

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Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials

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Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painlevé transcendent potentials

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Supersymmetric quantum mechanics and Painlevé IV equation

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Factorization method and new potentials from the inverted oscillator

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Supersymmetric partners of the harmonic oscillator with an infinite potential barrier

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SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations

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Solutions to the Painlevé V equation through supersymmetric quantum mechanics

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Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

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Generalized Hermite polynomials and monodromy-free Schrödinger operators

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A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator

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Exceptional orthogonal polynomials and the Darboux transformation

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HIGHER-ORDER SUSY, EXACTLY SOLVABLE POTENTIALS, AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS

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RATIONALLY-EXTENDED RADIAL OSCILLATORS AND LAGUERRE EXCEPTIONAL ORTHOGONAL POLYNOMIALS IN kTH-ORDER SUSYQM

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Two-step Darboux transformations and exceptional Laguerre polynomials

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A conjecture on exceptional orthogonal polynomials

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New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

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Combined state-adding and state-deleting approaches to type III multi-step rationally extended potentials: Applications to ladder operators and superintegrability

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Extended Krein-Adler theorem for the translationally shape invariant potentials

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Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials

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Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials

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Dirac electron in graphene under supersymmetry generated magnetic fields

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Construction of zero-energy states in graphene through the supersymmetry formalism

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Supersymmetry in Helmholtz optics

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Group approach to the paraxial propagation of Hermite-Gaussian modes in a parabolic medium

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Confluent chains of DBT: enlarged shape invariance and new orthogonal polynomials

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Supersymmetry in quantum mechanics: an extended view

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Mittag-Leffler coherent states

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On the completeness of coherent states generated by binomial distribution

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The good, the bad and the ugly coherent states through polynomial Heisenberg algebras

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SUSY QUANTUM MECHANICS WITH COMPLEX SUPERPOTENTIALS AND REAL ENERGY SPECTRA

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Factorization method for second order functional equations

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Second order \(q\)-difference equations solvable by factorization method

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Solutions of theq-deformed Schrödinger equation for special potentials

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The factorization of the (q,h)-difference operators

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Factorization method applied to the second order difference equations

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Q3997785

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Factorization of the hypergeometric-type difference equation on the uniform lattice

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Identifiers

zbMATH Open document ID

1425.81045

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DOI

10.1007/978-3-030-20087-9_2

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4973354