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 …

The Howe dual pair allows the characterization of the classical Fourier transform (FT) on the
space of rapidly decreasing functions as the exponential of a well-chosen element of such …

In this paper, exactly solvable model of the quantum harmonic oscillator is proposed. Wave
functions of the stationary states and energy spectrum of the model are obtained through the …

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 …

We define a Wigner distribution function for a one-dimensional finite quantum system, in
which the position and momentum operators have a finite (multiplicity-free) spectrum. The …

We explore a model for a one-dimensional quantum oscillator based on the Lie
superalgebra $\mathfrak {sl}(2| 1) $. For this purpose, a class of discrete series …

A superintegrable finite model of the quantum isotropic oscillator in two dimensions is
introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion …