Two quantum particles in one dimension involving the exchange operator

Abstract

In this work, after introducing the main algebraic and representative properties of the quantum mechanics with Dunkl derivative, two-particle system with exchange symmetry is studied. In this framework, a new deformed derivative involving the exchange operator is proposed. With the help of such an operator, the new deformed quantum theory for systems with two quantum particles in one dimension is developed. As physical applications of the present construction, systems with two quantum particles interacting via the harmonic potential and the delta-function potential well are considered in detail. The wave functions and the energy spectra for these potentials are derived. Finally, possible implications of our results on other application areas of research such as in interacting theories of either bosons or fermions are concisely discussed.