Exact mapping between charge-monopole and position-dependent effective mass systems via Pauli equation

Abstract

The main purpose of this work is to reproduce a quantum system charge-monopole utilizing position-dependent effective mass (PDM) system in the nonrelativistic regime via the Pauli equation. In this case, we substitute the exact charge-monopole wavefunction into the free PDM Pauli equation and then solve it for the mass distribution considering a radial dependence only, i.e., M = M(r). The resulting equations are nonlinear, and in such cases, we were able to numerically solve them, fixing θ0 and considering specific values of μ and m satisfying a given condition. The mapping was studied for eigenvalues starting from the minimal value j = μ − 1/2.

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.…”

Introdução à Física do Monopolo Magnético: uma abordagem clássica

“…, (50) na posição onde a carga atinge a distância mínima b de aproximação do monopolo (t = 0), os módulos das velocidades angular e radial são, respectivamente,…”

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.…”