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

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.

A New Method of Preparing Alkanethiol-Protected Gold Nanoparticals

In a new two-phase system (tetrahydrofuran/saturated NaCl aqueous solution) monolayer protected clusters (MPCs) were prepared.The AuCl- 4 anion in saturated electrolyte aqueous solution was transferred into the organic phase of tetrahydrofuran by tetra-n-butylammonium bromide ((C 4H 9) 4NBr) and was reduced quickly by sodium borohydride in the presence of alkanethiol.The functionalized MPCs were characterized by solubility,transmission electron microscopy (TEM),Fourier transform infrared spectroscopy (FTIR),energy-dispersive X-ray (EDX) analysis and UV-vis spectroscopy.Electrochemical measurements of MPCs in CH 2Cl 2 exhibited 7 pairs of reversible voltammetric waves within the potential range of -1.0 to 1.0V (vs Ag/AgCl),which was ascribed to the quantized capacitance charging of nanoparticle double layers.All the results show that the new preparing method is feasible.

Application of Electrodynamic Theory on Quantum Hall Effect

The quantum electrodynamic (QED) behaviour is studied for quantum Hall effect (QHE). Quantum theory with conjecture of fractional charge quantization (quantum dipole moment), eigenfunctions for fractional charge quantization at the surface of a twisted and twigged electron quanta and above its surface, fractional Fourier transform and Hermite function for fractional charge quantization is developed. With energy eigen value equation for QHE and with energy operator on an eigenfunction of a twisted and twigged electron quanta, the corresponding eigenfunctions are normalized with Schrodinger’s quantum wave mechanical equation for electric scalar and magnetic potentials, respectively (QED behavior). The fractional electric and magnetic fields with their corresponding potentials for the quantized fractional states in semiconducting hereto structures are theoretically calculated. Such mathematical expressions are in good agreement with experimental results of Nobel Prize winning scientists Klitzing, Haroche, Peter and Gruebber. Our results can also explain the hybridized states of orbits with emphasis on sigma and pi bonding and their corresponding antibonding orbitals as a manifestation of electrophilic and nucleophilic chemical reactions.