Generalized quantum conditions and coherent states
28 Mar 1998-Modern Physics Letters A (World Scientific Publishing Company)-Vol. 13, Iss: 10, pp 811-817
TL;DR: In this paper, possible modifications of the Calogero-Vasiliev quantum condition are considered and the problem of constructing coherent states is addressed, and a solution to the problem is given.
Abstract: We consider possible modifications of the Calogero–Vasiliev quantum condition and address the problem of construction of coherent states.
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TL;DR: In this paper, it was shown that the previously introduced algebraic approach to the self-similar potentials can be generalized to the q-algebras and the associated coherent states were investigated.
Abstract: Self-similar potentials generalize the concept of shape invariance which was originally introduced to explore exactly solvable potentials in quantum mechanics. In this paper it is shown that the previously introduced algebraic approach to the latter can be generalized to the former. The infinite Lie algebras introduced in this context are shown to be closely related to the q-algebras. The associated coherent states are investigated.
76 citations
TL;DR: In this paper, a graded Lie algebra structure analogous to Witten's SUSY quantum mechanical algebra is realized in which only annihilation operators participate, all expressed in terms of the Wigner annihilation operator of a related super-Wigner oscillator system.
Abstract: We extend Witten's supersymmetry (SUSY) formulation for Hamiltonian systems to a system of annihilation operator eigenvalue equations associated with the SUSY isotonic oscillator, which, as we show, define SUSY canonical supercoherent states containing mixtures of both pure bosonic and pure fermionic counterparts. Specifically, a graded Lie algebra structure analogous to Witten's SUSY quantum mechanical algebra is realized in which only annihilation operators participate, all expressed in terms of the Wigner annihilation operator of a related super-Wigner oscillator system.
9 citations
TL;DR: In this paper, noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn-Macfarlane q-oscillator.
Abstract: Noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn–Macfarlane q-oscillator. We consider ...
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01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
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TL;DR: In this article, the problem of N quantum-mechanical equal particles interacting pairwise by inverse cube forces (''centrifugal potential'') in addition to linear forces ( ''harmonical potential''), is considered in a onedimensional space.
Abstract: The problem of N quantum‐mechanical equal particles interacting pairwise by inverse‐cube forces (``centrifugal potential'') in addition to linear forces (``harmonical potential'') is considered in a onedimensional space. An explicit expression for the ground‐state energy and for the corresponding wavefunction is exhibited. A class of excited states is similarly displayed.
488 citations
TL;DR: In this article, it was shown that the postulate that the quantum mechanical operators obey the classical equations of motion uniquely determines the commutation relations of the Hamiltonian with the operator corresponding to any physical quantity gives the operator which corresponds to the time derivative of that quantity.
Abstract: The commutator of the Hamiltonian with the operator corresponding to any physical quantity gives the operator which corresponds to the time derivative of that quantity. One can ask, hence, whether the postulate, that the quantum mechanical operators obey the classical equations of motion, uniquely determines the commutation relations. The answer is found to depend on the form of the Hamiltonian and is in the negative for a free particle and for the harmonic oscillator.
422 citations
TL;DR: In this paper, the equivalence between anyons and anyons in the lowest Landau level was established using a complex representation of the deformed Heisenberg algebra underlying the Calogero model, and a construction based on supersymmetry was used to extend the operator method to include fermions.
166 citations