Ladder operators and squeezed coherent states of a three-dimensional generalized isotonic nonlinear oscillator

Abstract

Abstract. We explore squeezed coherent states of a 3-dimensional generalized isotonic oscillator whose radial part is the newly introduced generalized isotonic oscillator whose bound state solutions have been shown to admit the recently discovered X 1 -Laguerre polynomials. We construct a complete set of squeezed coherent states of this oscillator by exploring the squeezed coherent states of the radial part and combining the latter with the squeezed coherent states of the angular part. We also prove that the three mode squeezed coherent states resolve the identity operator. We evaluate Mandel's Q-parameter of the obtained states and demonstrate that these states exhibit sub-Possionian and super-Possionian photon statistics. Further, we illustrate the squeezing properties of these states, both in the radial and angular parts, by choosing appropriate observables in the respective parts. We also evaluate Wigner function of these three mode squeezed coherent states and demonstrate squeezing property explicitly.

Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations

“…The coherent states can be entangled [311][312][313][314], superposed [44][45][46][47]315], and constructed for non-Hermitian operators [86,87,316] in terms of either a bi-orthogonal basis [84,86,87,317] or noncommutative spaces [313,318,319], for which nonclassical properties can be found [87,107,320,321]. They have been also associated to super algebraic structures [314,[322][323][324][325][326], nonlinear oscillators [327][328][329], and solvable models [330][331][332][333][334][335][336][337][338][339][340][341][342].…”

Solvable potentials with exceptional orthogonal polynomials

“…The one-dimensional Schrödinger equation with the nonlinear oscillator potential (in the units = 2m = 1) − d 2 dx 2 + x 2 + 8(2x 2 − 1) (2x 2 + 1) 2 ψ n (x) = E n ψ n (x), ψ n (± ∞) = 0, −∞ < x < ∞, (1) has attracted attention over the past couple of decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The special interest arose from the structure of the exact closed-form solutions given by E n = 2n − 3, ψ n (x) = e −x 2 /2 1 + 2x 2 P n (x), n = 0, 3, 4, 5, .…”

“…To obtain exact solutions, within the application of supersymmetric quantum mechanics, of Schrödinger's equation with each extended potential families (6) and (7). To obtain exact solutions, within the application of supersymmetric quantum mechanics, of Schrödinger's equation with each extended potential families (6) and (7).…”

New $\mathcal {SU}(1,1)$ position-dependent effective mass coherent states for a generalized shifted harmonic oscillator

“…In particular, the most generalized CS which have been investigated in the literature are those associated with groups SU (2) and SU (1, 1) [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. For the usual SU (1, 1) group (which is the most elementary noncompact and non-Abelian simple Lie group) there are two sets of CS but not equivalent, namely: (CS1) the Barut-Girardello CS which are characterized by the complex eigenvalues α of the noncompact generator K − of the su(1, 1) algebra…”