Classical and quantum position-dependent mass harmonic oscillators

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

“…Then, the higher order Susy transformations can be also studied for the position-dependent mass systems we have presented in this work. The classical models of the harmonic oscillator and the Pöschl-Teller potentials have been also useful in the solving of mass-dependent systems [29,30] and in the construction of CS [31]. Of particular interest, the study of the Wigner function gives rise to a better understanding of the PDM coherent states [8,32].…”

A Study of Resonances in a One-Dimensional Model with Singular Hamiltonian and Mass Jumps

“…The matrices M i (a i ) are defined in (18). With the help of (18) and (17), we can derive the following recurrence relation:…”

“…This kind of Hamiltonians have received a lot of attention because of their interest in construction exactly solvable models [1][2][3][4][5][6][7][8][9][10][11]. Independently, systems with variable mass have lately acquired some attention in the literature [12][13][14][15][16][17][18][19][20][21][22]. The simplest one dimensional systems with variable mass are those in which the mass is constant except for a discontinuity or jump at a given point.…”

Position-dependent mass Lagrangians: nonlocal transformations, Euler–Lagrange invariance and exact solvability

“…Unlike the ordering ambiguity that arises in the kinetic energy term of the PDM von Roos quantum mechanical Hamiltonian, no such ordering ambiguities arise in the classical mechanical PDM Hamiltonian. Yet, it has been asserted that the resolution of the ordering ambiguity conflict in the PDM quantum Hamiltonian may be sought in the classical and quantum mechanical correspondence (cf., e.g., [12,17] for more details on this issue).…”