Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $\mathfrak{osp}\left(1|2\right)$: exact solution for the quantum harmonic oscillator with a position-dependent mass

E. I. Jafarov, S. M. Nagiyev, J. Van der Jeugt

We propose a new deformation of the quantum harmonic oscillator Heisenberg-Weyl algebra with a parameter $a>-1$. This parameter is introduced through the replacement of the homogen…