TITLE:
Eigenfunctions for a Quantum Wire on a Single Electron at Its Surface and in the Quantum Well with Beaded Fractional Quantized States for the Fractional Charges
AUTHORS:
Saleem Iqbal, Farhana Sarwar, Syed Mohsin Raza
KEYWORDS:
Fractional Charge Quantization, Fractional Fourier Transform, Hermite Polynomials, Sub Quanta of Electron, Spherical Bessel and Neumann Functions, Lagueree Polynomials
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.2,
February
25,
2016
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.