Half theory fractional angular momentum and the application of fractional derivatives to quantum mechanics

Abstract

In this paper, we review the fractional derivative and apply it to various problems in quantum mechanics. Among other things, we find fractional angular momentum, with “fractional spherical harmonics” as solutions to the squared quantum mechanical angular momentum operator, but with non-integer eigenvalues. These fractional functions might be interpreted as intermediary states visited by an orbiting electron as it jumps between the more stable, integer angular momentum values in an atom. Alternatively, these fractional states may be of interest in the mechanisms of chemical bonding. The justification for these new states, which are normalizable solutions to Hermitian operators, depends of course on experiment. We remember Feynmann’s statement about quantum mechanics, “Everything that is not expressly forbidden, is mandatory.”