Equivalence of String Classical and Quantum Energy beside Equivalence of Wave Packet and Relativistic Velocity in Eucleadian and Curved Space

Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.

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.

Quantum Theory of Mesoscopic Fractional Electric Fields in a Cavity of Viscous Medium

With conjecture of fractional charge quantization (quantum dipole/multiple moments), Fourier transform stretching, twisting and twigging of an electron quanta and waver strings of electron quanta, the mathematical expressions for mesoscopic fractional electron fields in a cavity of viscous medium and the associated quantum dielectric susceptibility are developed. Agreement of this approach is experimentally evidenced on barite and Fanja site molecular sieves. These findings are in conformity with experimental results of 2012 Physics Nobel prize winning scientists, Serge Haroche and David J. Wineland especially for cavity quantum electro-dynamics electron and its associated mesoscopic electric fields. The mover electron quanta strings lead to warping of space and time following the behaviour of quantum electron dynamics.