The question of Heisenberg uncertainty principle: Inevitable alternative interpretations and applications

With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a₀/100 and a₀/20 (a₀ is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a₀ and 49a₀ were demonstrated; the probability of locating the position (a) and momentum (p) increases with decreasing radii. The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen atom only. A relation between uncertainties and pa is for future study.