Distorted Heisenberg algebra and coherent states for isospectral oscillator Hamiltonians

Abstract

The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent of a parameter w ≥ 0. We name it distorted Heisenberg algebra, where w is the distortion parameter. The corresponding coherent states for an arbitrary w are derived, and some particular examples are discussed in full detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.

Graphene coherent states

“…It is important to remark that, in a sense, the graphene coherent states remind the multiphoton coherent states [28,29,30,31,32,33], which appear from realizations of the Polynomial Heisenberg Algebras (PHA) for the harmonic oscillator [24,25,26,34,35,36]. In that formalism, the Hilbert space decomposes as a direct sum of m orthogonal subspaces, on each of which it is possible to construct the corresponding coherent states as superpositions of standard coherent states, while in the case of this paper the minimum energy states can be isolated from the remaining Hilbert subspace, depending on the values taken by f (n).…”

“…(27) it takes its minimum at α = 0, while for those in Eqs. (29) and (31) their maxima are reached at the same point; this is so since the lowest energy eigenstate involved in the corresponding linear combination is different if different families of coherent states are taken into account (see also [24,25,26]). …”

SU(1,1) Coherent States for Position-Dependent Mass Singular Oscillators

“…[21] and [22]). These algebras have been applied in the construction of a new kind of CS connected with the linear oscillator and its Susy-partners [23][24][25][26][27][28]. Quite recently, it has been shown that non-linear Susy algebras can be linearized to exhibit the Heisenberg-Weyl structure.…”

Ladder operators for isospectral oscillators

“…10 corresponds to setting w 1 = w and w n = 1 for n ≥ 2, so that W n+1 = (w + n). Thereforẽ a 1 reduces, in this special case, to a closed-form expression -namely, the operator C w defined in Eqs.…”