How Fractional Charge on an Electron in the Momentum Space is Quantized?

Abstract

With our conjecture on charge quantization (quantum dipole moment in a momentum space) and using Fractional Fourier Transform (FRFT) analysis on Hermite Polynomials (usually used for quantum oscillators), we obtained energy pro?les (eigenfunctions) for fractional quantum states on the continuously changing surface of the electron. The charge on an electron as a physical constant and a single entity is degenerate because it always resides on the surface. The charge is fractionally quantized in momentum space. The continuous charging surface of the electron is due to competition between the centrifugal and electodynamic potentials. The fractional quantized states of charges in the momentum space are the manifestations of gyroscopic constants,   twisting and twigging of energy profiles (quantum electrodynamic behavior), oscillatory behavior of energy associated with degeneracy and indeed the position of fractional quanta in terms of rotational vector,  in complex plane.