Two types of q‐deformed Wigner algebra

In this paper we introduce two types of q‐deformed Wigner algebras. One is q‐deformation of Wigner algebra with q‐reflection symmetry and another is q‐deformation of Wigner algebra with reflection symmetry. For two types of q‐deformed Wigner algebras, we investigate the representation and the eigenvalue of the position operator. Like q‐calculus, we introduce the (q; ν)‐ numbers, (q; ν)‐derivatives and (q; ν)‐Hermite polynomials for two algebras. For the deformation parameter q = 1 ‐ ϵ with small ϵ, we discuss the thermodynamics of the particle obeying the q‐deformed Wigner algebra.