Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

Abstract

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 factorization method of the Hamiltonian under consideration, we have found three basis elements of this algebra. The algebra defined through those basis elements is an su (1,1) Heisenberg–Lie algebra. Different special cases and the limit relations from the basis elements to the Heisenberg–Weyl algebra of the nonrelativistic quantum harmonic oscillator are discussed, too.