A New Nonrelativistic Investigation for Interactions in One-Electron Atoms With Modified Inverse-Square Potential: Noncommutative Two and Three Dimensional Space Phase Solutions at Planck’s and Nano-Scales

Abstract

It is well-known, that, the modern quantum mechanics, satisfied a big successful in the last few years, for describing atoms, nuclei, and molecules and their spectral behaviors based on three fundamental equations: Schrödinger, Klein-Gordon and Dirac. Schrödinger equation rest the first and the latest in terms of interest, it is playing a crucial role in devising well-behaved physical models in different fields of physics and chemists, many potentials are treated within the framework of nonrelativistic quantum mechanics based on this equation in two, three and D generalized spaces [1-30], the quantum structure based to the ordinary canonical commutations relations (CCRs) in both Schrödinger and Heisenberg (the operators are depended on time) pictures (CCRs), respectively, as: