On Supersymmetric Quantum Mechanics

Kibler, M.; Daoud, Mohammed

doi:10.1007/978-94-017-0448-9_5

Cited by 3 publications

(2 citation statements)

References 91 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The A {κ} r-parameter algebra covers the cases of (i) the extended harmonic oscillator algebra [21], (ii) the fractional oscillator algebra [27] and (iii) the W k algebra introduced in the context of fractional supersymmetric quantum mechanics of order k [28,30]. As a particular case, the algebra A {κ} with κ 1 = κ and r = 1 is nothing but the A κ algebra worked out in [18] and corresponding to…”

Section: The a {κ} Algebramentioning

confidence: 99%

Bosonic andk-fermionic coherent states for a class of polynomial Weyl–Heisenberg algebras

Daoud¹,

Kibler²

2012

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The aim of this article is to constructà la Perelomov andà la Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This generalized Weyl-Heisenberg algebra, noted A {κ} , depends on r real parameters and is an extension of the A κ one-parameter algebra (Daoud M and Kibler M R 2010 J. Phys. A: Math. Theor. 43 115303) which covers the cases of the su(1, 1) algebra (for κ > 0), the su(2) algebra (for κ < 0) and the h 4 ordinary Weyl-Heisenberg algebra (for κ = 0). For finite-dimensional representations of A {κ} and A {κ},s , where A {κ},s is a truncation of order s of A {κ} in the sense of Pegg-Barnett, a connection is established with k-fermionic algebras (or quon algebras). This connection makes it possible to use generalized Grassmann variables for constructing certain coherent states. Coherent states of the Perelomov type are derived for infinitedimensional representations of A {κ} and for finite-dimensional representations of A {κ} and A {κ},s through a Fock-Bargmann analytical approach based on the use of complex (or bosonic) variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in the case of infinite-dimensional representations of A {κ} . In contrast, the construction ofà la Barut-Girardello coherent states for finite-dimensional representations of A {κ} and A {κ},s can be achieved solely at the price to replace complex variables by generalized Grassmann (or k-fermionic) variables. Some of the results are applied to su(2), su(1, 1) and the harmonic oscillator (in a truncated or not truncated form).

show abstract

Section: The a {κ} Algebramentioning

confidence: 99%

Bosonic andk-fermionic coherent states for a class of polynomial Weyl–Heisenberg algebras

Daoud¹,

Kibler²

2012

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…2 by applying J ν=3 + three times on the ground state, Ψ k −3 ,0 (r, k −3 ), of V (−3) and obtain the third excited state of V (0). A more recent and detailed review of the SUSY formalism can be found in [19].…”

Section: Effective Morse Potentials Generated Bymentioning

confidence: 99%

Analysis of the spectrum generating algebra method for obtaining energy spectra

Cordero

Daboul

2005

Journal of Mathematical Physics

View full text Add to dashboard Cite

We analyze and clarify how the SGA (spectrum generating algebra) method has been applied to different potentials. We emphasize that each energy level E ν obtained originally by Morse belongs to a different so(2, 1) multiplet. The corresponding wavefunctions Ψ ν are eigenfuntions of the compact generators J ν 0 with the same eigenvalue k 0 , but with different eigenvalues q ν of the Casimir operators Q. We derive a general expression for all effective potentials which have Ψ λ ν ,ν+m (r) ∝ (J ν + ) m Ψ λ ν ,ν (r) as eigenfunctions, without using supersymmetry formalism. The different actions of SGA is further illustrated by two diagrams.

show abstract

Bibliography of Publications

Beebe¹

1995

Cultures, Ideologies, and the Dictionary

View full text Add to dashboard Cite

On Supersymmetric Quantum Mechanics

Cited by 3 publications

References 91 publications

Bosonic andk-fermionic coherent states for a class of polynomial Weyl–Heisenberg algebras

Bosonic andk-fermionic coherent states for a class of polynomial Weyl–Heisenberg algebras

Analysis of the spectrum generating algebra method for obtaining energy spectra

Bibliography of Publications

Contact Info

Product

Resources

About