Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry

Ali, S. Twareque; Багарелло, Фабио

doi:10.1063/1.2898117

Cited by 23 publications

(29 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us take V 1 (x, y) = W 1 (x, y) = − x 2 , V 2 (x, y) = W 2 (x, y) = − y 2 . If we further take α = γ = α ′ = γ ′ = 1 √ 2 we recover exactly the usual situation, [24]. Moreover, we go back to bosonic rather than pseudo-bosonic commutation relations.…”

Section: Generalized Landau Levels (Gll)mentioning

confidence: 59%

See 1 more Smart Citation

Pseudo-Bosons, So Far

Багарелло

2011

Reports on Mathematical Physics

Self Cite

View full text Add to dashboard Cite

In the past years several extensions of the canonical commutation relations have been proposed by different people in different contexts and some interesting physics and mathematics have been deduced. Here, we review some recent results on the so-called pseudobosons. They arise from a special deformation of the canonical commutation relation [a, a † ] = 1 1, which is replaced by [a, b] = 1 1, with b not necessarily equal to a † . We start discussing some of their mathematical properties and then we discuss several examples.Under the above assumptions, and if we chose the normalization of Ψ 0 and ϕ 0 in such a way that Ψ 0 , ϕ 0 = 1, we find that Ψ n , ϕ m = δ n,m = d j=1 δ n j ,m j .(2.4)This means that the sets F Ψ = {Ψ n } and F ϕ = {ϕ n } are biorthogonal and, because of this, the vectors of each set are linearly independent. If we now call D ϕ and D Ψ respectively the linear 3 span of F ϕ and F Ψ , and H ϕ and H Ψ their closures, then f = n

show abstract

Section: Generalized Landau Levels (Gll)mentioning

confidence: 59%

“…where α γ = 1 2 and α ′ γ ′ = 1 2 . Thus, the operators generalizing the Landau Hamiltonians in [24] are…”

Section: Generalized Landau Levels (Gll)mentioning

confidence: 99%

Pseudo-Bosons, So Far

Багарелло

2011

Reports on Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…For information concerning the last states, the reader can seek e.g. [21,22,23] and references therein.…”

Section: Case With F (1) =mentioning

confidence: 99%

Graphene coherent states

Díaz-Bautista

2017

Eur. Phys. J. Plus

View full text Add to dashboard Cite

In this paper we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of all, we will identify the appropriate annihilation and creation operators. Then, we will derive the coherent states as eigenstates of the annihilation operator, with complex eigenvalues. Several physical quantities, as the Heisenberg uncertainty product, probability density and mean energy value, will be as well explored.

show abstract

“…This is a problem which has been addressed in the literature by several authors and in several different ways, see [8,12,14,15] and references therein. These differences arise mainly because of the non-uniqueness of the definition of what a CS should be.…”

Section: Gazeau-klauder Like Coherent Statesmentioning

confidence: 99%