Deformed quantum mechanics with extended Dunkl derivative

In this research, we investigate the extended Dunkl quantum mechanics with two parameters. We apply this formalism to study general quantum phenomena. Using cartesian coordinate, we calculate the solution to problem of a spinless particle confined to a box in three dimensions. Then, we derive the creation and annihilation operators to analyze harmonic oscillator in three dimensions via algebraic approach. Subsequently, utilizing the same operators and the generators of [Formula: see text] Lie algebra, we examine the Dirac harmonic oscillator in [Formula: see text] dimension. Finally, we construct the hydrodynamical formulation of the extended Dunkl quantum mechanics by deriving continuity and quantum Hamilton–Jacobi equations.