Abstract
We developed energy profiles for the fractional quantized states both on the surface of electron due to overwhelming centrifugal potentials and inside the electron at different locations of the quantum well due to overwhelming attractive electrodynamic potentials. The charge as a physical constant and single entity is taken as density and segments on their respective sub-quanta (floats on sub quanta) and hence the fractional charge quantiz at in. There is an integrated oscillatory effect which ties all fractional quantized states both on the surface and in the interior of the volume of an electron. The eigenfunctions, i.e., the energy profiles for the electron show the shape of a string or a quantum wire in which fractional quantized states are beaded. We followed an entirely different approach and indeed thesis to reproducing the eigenfunctions for the fractional quantized states for a single electron. We produced very fascinating mathematical formulas for all such cases by using Hermite and Laguerre polynomials, spherical based and Neumann functions and indeed asymptotic behavior of Bessel and Neumann functions. Our quantization theory is dealt in the momentum space.
Highlights
The inside of the electron is treated like a potential well with its depth equivalent to radius re and that the charge above it is fractionally quantized
Each fractional quantized state is a manifestation of sub quanta due to change in mass distribution
This happens in the momentum space just like the Compton and Photoelectric effects
Summary
The inside of the electron is treated like a potential well with its depth equivalent to radius re and that the charge above it is fractionally quantized. The question why and how this happens could be answered by considering that the centrifugal potential is dominating over the electrodynamic potential, as a consequence of which,quantum well with a depth re is becoming shallow and that the segmented masses of electron are shifting on the surface but coupled with a string. This coupling, is due to gyroscopic behaviour of an electron. The gyroscopic behaviour of an electron causes the c constant entity of charge to become degenerate and fractionally quantized above its surface ( due to segmented mass distribution but coupled with a string at different locations just above the surface). The charge is fragmented and floats on their respective sub quanta
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