We present an exact solution of a confined model of the non-relativistic quantum harmonic
oscillator, where the effective mass and the angular frequency are dependent on the …

We constructed a new model of the non-relativistic quantum harmonic oscillator within the
canonical approach. It is asymmetrically confined into the infinitely high potential well …

Two exactly-solvable confined models of the completely positive oscillator-shaped quantum
well are proposed. Exact solutions of the position-dependent mass Schr\" odinger equation …

Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-
dependent effective mass is constructed. Selecting the starting point as a well-known …

sh (2| 2)⁠, known as the Heisenberg–Weyl superalgebra or “the algebra of supersymmetric
quantum mechanics,” and its Fock representation. The model offers some freedom in the …

In this work, we present a rigorous mathematical scheme for the derivation of the sth-order
perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed …

Exactly-solvable confined model of the non-relativistic quantum harmonic oscillator is
proposed. Free Hamiltonian of the system under study has a form of the Gora-Williams …

A superintegrable, discrete model of the quantum isotropic oscillator in two-dimensions is
introduced. The system is defined on the regular, infinite-dimensional ${\mathbb {N}}\times …

This Viewpoint relates to articles by LC Biedenharn (1989 J. Phys. A: Math. Gen. 22 L873)
and AJ Macfarlane (1989 J. Phys. A: Math. Gen. 22 4581) and was published as part of a …

We investigate new models for a finite quantum oscillator based upon the Lie superalgebra,
where the position and momentum operators are represented as odd elements of the …