Position-dependent effective mass system in a variable potential: displacement operator method

Abstract

Within the framework of the translation operator for a quantum system with position-dependent mass, we examine the quantum state of a position-dependent mass system in a variable potential. By imposing conditions of resolvability, we arrive at a potential with a quartic and a quadratic term. It emerges naturally that the energy eigen states of the system are negative. We have found the quantum mechanical quantities: energy spectrum, eigen functions and uncertainty relation. These quantities depend on the parameters of the potential.

A position-dependent mass harmonic oscillator and deformed space

“…and consequently a particle with PDM. This deformed momentum operator has been used to discuss a system with PDM for different potentials in the quantum formalism [8][9][10][11][14][15][16][17][18][19][20].…”

Position-dependent mass systems: Classical and quantum pictures

“…[37][38][39][40][41][42][43][44][45]. Further details concerning the properties of quantum systems with position-dependent mass can be consulted in, e.g., [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64].…”

Transmission through graded interfaces in the displacement operator method

“…In the displacement operator approach introduced by Costa et al [12], to arrive at an effective variable mass, one starts from a constant mass system which is assumed to undergo non-additive translations such that the deformed momentum operator describing such displacements gives rise to a position-dependent effective mass. This formalism has been addressed for a system in null and constant potentials [13], double well [14], parabolic [15] and Coulomb-like [16] potentials. Its classical field theory has also been established [17] .…”