Investigation of Some Quantum Mechanics Problems with kappa-Translation Symmetry

Abstract

In this paper the kappa-deformed translation symmetry is considered based on the kappa-addition appearing in the kappa-deformed statistical mechanics. The deformed quantum theory with kappa-translation symmetry is constructed. The plane wave kappa-translation symmetry is constructed. The Ramsauer-Townsend effect and one dimensional box problem in the deformed quantum theory with kappa-translation symmetry is discussed. Finally, the quantum harmonic oscillator problem in the deformed quantum theory with kappa-translation symmetry is discussed.