Author/Authors :
Jafarov, Elchin I. Institute of Physics - Azerbaijan National Academy of Sciences, Baku, Azerbaijan , Jafarova, Aynura M. Institute of Mathematics and Mechanics - Azerbaijan National Academy of Sciences, Baku, Azerbaijan , Oste, Roy Department of Applied Mathematics - Computer Science and Statistics - Ghent University, Krijgslaant, Belgium
Abstract :
An exactly solvable model of the one-dimensional quantum harmonic oscillator
confined in a box with infinite walls is constructed. We have found explicit expressions
of the non-equidistant energy spectrum as well as stationary states wavefunctions in both
momentum and position configuration spaces. It is shown that they are expressed through
continuous q-Hermite polynomials. We have also found an explicit expression for the kernel
of the finite-continuous Fourier transform between these two representation spaces.
