On extended umbral calculus, oscillator-like algebras and Generalized Clifford Algebra

Abstract

Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized Clifford algebras also in the context of azimuthal quantization of angular momentum which was interpreted afterwards as the finite dimensional quantum mechanics .