Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablele...Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablelength. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentumspace representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and thecorresponding 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 penningtrap.展开更多
文摘Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablelength. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentumspace representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and thecorresponding 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 penningtrap.
