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Families of superintegrable Hamiltonians constructed from exceptional polynomials
Families of superintegrable Hamiltonians exceptional polynomials Mathematical Physics
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2012/6/19
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum t...
Resolutions of identity for some non-Hermitian Hamiltonians II: proofs
non-Hermitian quantum mechanics exceptional points resolution of identity
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2011/9/23
Abstract: This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated func...
Resolutions of identity for some non-Hermitian Hamiltonians I: exceptional point in continuous spectrum
non-Hermitian quantum mechanics exceptional points resolution of identity
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2011/9/23
Abstract: Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entir...
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
multiple Charlier polynomials non-Hermitian Hamiltonians algebraic model
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2011/7/26
Abstract: A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of mult...
Integrable relativistic systems given by Hamiltonians with momentum-spin-orbit coupling
Integrable relativistic systems Hamiltonians momentum-spin-orbit coupling
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2011/7/26
Abstract: In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We inte...
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
Hierarchy of integrable Hamiltonians nonlinear n-wave interaction Exactly Solvable and Integrable Systems
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2011/7/26
Abstract: In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special...
Ground states of semi-relativistic Pauli-Fierz and no-pair Hamiltonians in QED at critical Coulomb coupling
Existence of ground states exponential localization no-pair Hamiltonian quantum electrodynamics
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2011/7/26
Abstract: We consider the semi-relativistic Pauli-Fierz Hamiltonian and a no-pair model of a hydrogen-like atom interacting with a quantized photon field at the respective critical values of the Coulo...