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.
Quantum theory with conjecture of fractional charge quantization, eigenfunctions for fractional charge quantization, fractional Fourier transform, Hermite function for fractional charge quantization, and eigenfunction for a twisted and twigged electron quanta is developed and applied to resistivity, dielectricity, giant magneto resistance, Hall effect and conductance. Our theoretical relationship for quantum measurements is in good conformity and in agreement with most of the experimental results. These relationships will pave a new approach to quantum physics for deciphering measurements on single quantum particles without destroying them. Our results are in agreement with 2012 Physics Nobel Prize winning Scientists, Serge Haroche and David J. Wineland.
Abstract( ) ∂ ∂t η , i.e., the unitary operator on shear modulus yields the variations in the curvature of time due to which simultaneous quantization, and depinning of dislocations occur from Peierls barrier in cubic crystals.
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