Realization of the Annihilation Operator for an Oscillator-Like System by a Differential Operator and Hermite-Chihara Polynomials

Borzov, V. V.; Damaskinsky, E. V.

doi:10.1080/10652460213751

Cited by 20 publications

(26 citation statements)

References 14 publications

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“…Also, the construction of the ladder operator is an interesting mathematical problem connected with (quantum) group theory [17], and has its applications in physical chemistry [18].…”

Section: Discussionmentioning

confidence: 99%

Harmonic oscillator with minimal length uncertainty relations and ladder operators

2003

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“…Also, the construction of the ladder operator is an interesting mathematical problem connected with (quantum) group theory [17], and has its applications in physical chemistry [18].…”

Section: Discussionmentioning

confidence: 99%

Harmonic oscillator with minimal length uncertainty relations and ladder operators

2003

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“…As was said previously, in order to find bosonic ladder operators [20][21][22] related to the eigenfunctions we were in search for, the knowledge on the detailed form of the normalization factor is essential. Thus, after we utilize the normalization properties of the Jacobi and Laguerre polynomials, we are left with the normalized version of the eigenfunctions (25) of the model Hamiltonian (1),…”

Section: Ladder Operatorsmentioning

confidence: 99%

“…In calculating ( 22), we shall make use of the fact that the successive application of the operator T − to the states (21) leads to an expression of the form…”

Section: Bargmann Representation Analysismentioning

confidence: 99%

Quantization and conformal properties of a generalized Calogero model

et al. 2007

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We analyze a generalization of the quantum Calogero model with the underlying conformal symmetry, paying special attention to the two-body model deformation. Owing to the underlying SU (1, 1) symmetry, we find that the analytic solutions of this model can be described within the scope of the Bargmann representation analysis and we investigate its dynamical structure by constructing the corresponding Fock space realization. The analysis from the standpoint of supersymmetric quantum mechanics (SUSYQM), when applied to this problem, reveals that the model is also shape invariant. For a certain range of the system parameters, the two-body generalization of the Calogero model is shown to admit a one-parameter family of self-adjoint extensions, leading to inequivalent quantizations of the system. PACS number(s): 02.30. Ik, 03.65.Fd,

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“…so that λ N = λ 0 = 1 2 N. Using the results obtained in [7] it can be shown that difference equation (8) for Krawtchouk polynomials K n (x; p, N ) is equivalent to eigenvalue equation for Hamiltonian H in the space H p,N . For obtaining the explicit expression of this operator as a difference operator in H p,N it is convenient to compare our variant of Krawtchouk oscillator with one was considered in [4].…”

mentioning

confidence: 99%

Coherent states of Krawtchouk oscillator and beyond

Borzov¹,

Damaskinsky²

2006

DAYS on DIFFRACTION 2006

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In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. . These polynomials provide an important example of the classical orthogonal polynomials of discrete variable. It is very attractive for some applications that they can be considered as finitedimensional approximations of the Hermite and Charlier polynomials [3]. In the papers [6] -[11] the authors proposed a new approach to construction of oscillator-like systems (so-called generalized oscillators) connected with given family of orthogonal polynomials. Furthermore, in these papers was introduced and investigated the coherent states for this type oscillators. Now in the frame of our approach we construct the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator)

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Realization of the Annihilation Operator for an Oscillator-Like System by a Differential Operator and Hermite-Chihara Polynomials

Cited by 20 publications

References 14 publications

Harmonic oscillator with minimal length uncertainty relations and ladder operators

Harmonic oscillator with minimal length uncertainty relations and ladder operators

Quantization and conformal properties of a generalized Calogero model

Coherent states of Krawtchouk oscillator and beyond

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