Exact Solution of D-Dimensional Klein-Gordon Oscillator with Minimal Length

Specific modifications of the usual canonical commutation relations between position and momentum operators have been proposed in the literature in order to implement the idea of the existence of a minimal observable length. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentum space representation the Klein–Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and the corresponding momentum space wave function are obtained. Following Chang et al. (Phys. Rev. D 65 (2002) 125027), we discuss constraint that can be placed on the minimal length by measuring the energy levels of an electron in a penning trap.