Exact solution in the Heisenberg picture and annihilation-creation operators

Abstract

The annihilation-creation operators of the harmonic oscillator, the basic and most important tools in quantum physics, are generalised to most solvable quantum mechanical systems of single degree of freedom including the so-called `discrete' quantum mechanics. They admit exact Heisenberg operator solution. We present unified definition of the annihilation-creation operators (a^{(\pm)}) as the positive/negative frequency parts of the exact Heisenberg operator solution.

10 pages, no figures. Abstract, Introduction revised; Conclusion added; Document-class changed. To appear in Phys. Lett. B

References in corpus (11)

• Supersymmetry and Quantum Mechanics
• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Temporally stable coherent states for infinite well and Pöschl-Teller potentials
• Shape-invariant potentials and an associated coherent state
• Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
• Coherent states à la Klauder-Perelomov for the Pöschl-Teller potentials
• The structure relation for Askey-Wilson polynomials
• Shape Invariant Potentials in "Discrete Quantum Mechanics"
• An Algebraic Construction of Generalized Coherent States for Shape-Invariant Potentials
• Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials
• Generalized coherent and intelligent states for exact solvable quantum systems

Cited by in corpus (34)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
• Orthogonal Polynomials from Hermitian Matrices
• Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
• Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
• Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
• Modification of Crum's Theorem for `Discrete' Quantum Mechanics
• Discrete Quantum Mechanics
• Multi-indexed (q-)Racah Polynomials
• Extensions of solvable potentials with finitely many discrete eigenstates
• Exactly Solvable Birth and Death Processes
• Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
• Orthogonal Polynomials from Hermitian Matrices II
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
• q-oscillator from the q-Hermite Polynomial
• Casoratian Identities for the Wilson and Askey-Wilson Polynomials
• Quasi Exactly Solvable Difference Equations
• Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
• Multi-indexed Meixner and Little $q$-Jacobi (Laguerre) Polynomials
• Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
• Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators
• Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice
• Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
• Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
• Perturbations around the zeros of classical orthogonal polynomials
• Exact Heisenberg operator solutions for multi-particle quantum mechanics
• Exactly and quasi-exactly solvable `discrete' quantum mechanics
• New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and $q$-Racah types
• Non-polynomial extensions of solvable potentials a la Abraham-Moses
• Exactly Solvable Quantum Mechanics
• Spectral intertwining relations in exactly solvable quantum-mechanical systems
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types