A semi-classical study of some generalized commutators

Abstract

Our aim in this paper is to find the observable effects of the generalized commutators. For this purpose we investigate two problems in quantum mechanics with minimal length procedure. Firstly, we study hydrogen atom energy levels via minimal length uncertainty relation algebra. From comparing our results, with experimental data we estimate an upper limit for minimal length. Secondly, we investigate statistical mechanics and density of states in phase space via minimal length uncertainty relation and find a correction for white dwarf mass limit. Finally, we study classical implication of minimal momentum uncertainty relations. With this procedure we have corrected the Keplerian third law and some results have been obtained.

Keywords

• Minimal length uncertainty relations
• semi classical approximation
• quantum gravity