Quaternionic vector coherent states and the supersymmetric harmonic oscillator

Thirulogasanthar, K.; Krzyżak, Adam; Katatbeh, Qutaibeh

doi:10.1007/s11232-006-0125-2

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…A similar result is worked out for the supersymmetric harmonic oscillator VCSs [17]. We can deduce the measure corresponding to the NCVSs | Z; τ ± ; ± by setting dµ( Z) = dµ(Z).…”

Section: Constraining the Ladder Operator Algebra Such That [Asupporting

confidence: 61%

See 1 more Smart Citation

New formulation of nonlinear vector coherent states off-deformed spin–orbit Hamiltonians

Geloun¹,

Hounkonnou²

2007

J. Phys. A: Math. Theor.

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“…A similar result is worked out for the supersymmetric harmonic oscillator VCSs [17]. We can deduce the measure corresponding to the NCVSs | Z; τ ± ; ± by setting dµ( Z) = dµ(Z).…”

Section: Constraining the Ladder Operator Algebra Such That [Asupporting

confidence: 61%

“…As particular NVCSs defined over the matrix domain, let us consider now quaternionic NVCSs recovered for the following matrix representation [2,17],…”

Section: Constraining the Ladder Operator Algebra Such That [Amentioning

confidence: 99%

New formulation of nonlinear vector coherent states off-deformed spin–orbit Hamiltonians

Geloun¹,

Hounkonnou²

2007

J. Phys. A: Math. Theor.

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“…The measures (138) and ( 145) have been discussed in Refs [33,11]. Finally, the same comments about solvable deformed theories as over normal NVCSs remain true also for quaternion NVCSs.…”

Section: Matrix Formulationmentioning

confidence: 81%

New classes of nonlinear vector coherent states of generalized spin-orbit Hamiltonians

Geloun,

Hounkonnou

2009

Preprint

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This paper deals with an extension of our previous work [J. Phys. A: Math. Theor. 40 F817] by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau-Klauder type associated with generalized spin-orbit Hamiltonians. We define an annihilation operator which takes into account the finite dimensional space of states induced by the k-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their "dual" counterparts are also discussed. Still by using the Hilbert space structure, a new family of NVCSs parameterized by unit vectors of the S 3 sphere has been identified without making use of the annihilation operator.

show abstract

“…Measures (137) and (144) have been discussed in [11,33]. Finally, the same comments about solvable deformed theories as over normal NVCSs remain true also for quaternion NVCSs.…”

Section: Matrix Formulationmentioning

confidence: 84%

New classes of nonlinear vector coherent states of generalized spin–orbit Hamiltonians

Geloun

Hounkonnou

2009

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

This paper deals with an extension of our previous work (Ben Geloun and Hounkonnou 2007 J. Phys. A: Math. Theor. 40 F817) by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau–Klauder type associated with generalized spin–orbit Hamiltonians. We define an annihilation operator which takes into account the finite-dimensional space of states induced by the k-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their ‘dual’ counterparts are also discussed. Also, by using the Hilbert space structure, a new family of NVCSs parametrized by unit vectors of the S3 sphere has been identified without making use of the annihilation operator.

show abstract

Quaternionic vector coherent states and the supersymmetric harmonic oscillator

Cited by 6 publications

References 15 publications

New formulation of nonlinear vector coherent states off-deformed spin–orbit Hamiltonians

New formulation of nonlinear vector coherent states off-deformed spin–orbit Hamiltonians

New classes of nonlinear vector coherent states of generalized spin-orbit Hamiltonians

New classes of nonlinear vector coherent states of generalized spin–orbit Hamiltonians

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