Relativistic problem of scalar particles in deformed space

Abstract

In this thesis we have treated the problem of the Klein-Gordon oscillator (KGO) with the generalized uncertainty principle (GUP) in deformed space. In the first case we deal with the problem of the scalar particle in the case of the free Klein-Gordon oscillator (ε = 0), the energy spectrum E is represented as function n and the wave function φ (x) is obtaind by the Hermite polynomial H n n (x). In the 2nd case, we have solved the equation of the Klein-Gordon oscil- lator in the presence of the external electric field ε in the deformed space, where the energy spectrum E is given as a function of power of n due to minimal length effect and the wave function φ n (p) is defined in term of the Gegenbaouer plynomial C λ n n (p). The borderline cases are deduced and confirmed the results obtained, recently the term probabilities Z, U, F, C, S have been calculated. As conclusion to this work we introduced the path intgral treatment of the Klein-Gordon oscillator in absence of the external electric field ε in the deformed space. Key words : relativistic quantum mechanics, Klein Gordon equation , regular spaces, deformed spaces, minimal length.