Supersymmetric approach to coherent states for nonlinear oscillator with spatially dependent effective mass

Abstract

A nonlinear oscillator with variable mass is studied in the approach of Supersymmetric quantum mechanics. Ladder operators in association with the shape invariance condition allowed us to find the coherent states of the system in the sense of Barut and Girardello. The statistical properties of these particular states are studied using the probability of distribution. In addition, the vibrational partition function is calculated. We see that the thermodynamic functions of the system such as mean energy and entropy depend on the nonlinearity parameter, except for the specific heat.

κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass

“…2 Further studies in noncommuting quantum spaces led to a Schrödinger equation with a position-dependent effective mass (PDM). 3 Along the last decades, the PDM systems have attracted attention because of their wide range of applicability in semiconductor theory, [4][5][6][7] nonlinear optics, 8 quantum liquids, 9,10 inversion potential for NH 3 in density functional theory, 11 particle physics, 12 many body theory, 13 molecular physics, 14 Wigner functions, 15 relativistic quantum mechanics, 16 superintegrable systems, 17 nuclear physics, 18 magnetic monopoles, 19,20 astrophysics, 21 nonlinear oscillations, [22][23][24][25][26][27][28][29][30][31] factorization methods and supersymmetry, [32][33][34][35][36] coherent states, [37][38][39] etc.…”

$κ$-Deformed quantum and classical mechanics for a system with position-dependent effective mass

“…Although we have applied the mapping approach to a κ-deformed space in order to study the quantum Mathews-Lakshmanan oscillator, it is important to mention that other equivalent approaches can be found in the literature. For instance, factorization methods, supersymmetry and coherent states have also been investigated for this nonlinear oscillator (see [34][35][36][37][38] and references therein).…”

“…2 Further studies in noncommuting quantum spaces led to a Schrödinger equation with a position-dependent effective mass (PDM). 3 Along the last decades the PDM systems have attracted attention because of their wide range of applicability in semiconductor theory, [4][5][6][7] nonlinear optics, 8 quantum liquids, 9,10 inversion potential for NH 3 in density functional theory, 11 particle physics, 12 many body theory, 13 molecular physics, 14 Wigner functions, 15 relativistic quantum mechanics, 16 superintegrable systems, 17 nuclear physics, 18 magnetic monopoles, 19,20 astrophysics, 21 nonlinear oscillations, [22][23][24][25][26][27][28][29][30][31] factorization methods and supersymmetry, [32][33][34][35][36] coherent states, [37][38][39] etc.…”

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

“…Another important issue in quantum mechanics is the concept of position-dependent effective mass. Along the last few decades, it has attracted the interest of several researchers due to its wide applicability: semiconductors, [16][17][18][19][20][21][22][23] nonlinear optics, 24 quantum liquids, 25 many body theory, 26 molecular physics, 27,28 quantum information entropy, 29 relativistic quantum mechanics, 30,31 nuclear physics, 32 magnetic monopoles, 33,34 nonlinear oscillations, [35][36][37][38][39][40][41][42] semiconfined harmonic oscillator, [43][44][45][46] factorization methods and supersymmetry, [47][48][49][50][51] coherent states, [52][53][54][55] etc. The mathematical description of quantum systems with a) Electronic mail: bruno.costa@ifsertao-pe.edu.br b) Electronic mail: ignacio.gomez@uesb.edu.br c) Electronic mail: biswanathrath10@gmail.com position-dependent mass (PDM) is based on the non-commutativity between the mass and the linear momentum operators, which leads to the ordering problem for the kinetic energy operator.…”