Derivation of Magnetic Field and Hall Voltage Quantization by Different Methods

Abstract

Quantization of magnetic and electric and magnetic field is one of the challenges that faces condensed matter. Magnetic quantization for super conducting materials suffers from noticeable setbacks. The first one is related to the fact that the magnetic flux quantization is based on assuming the current density to be zero, which is in conflict with the experimentally observed current flow. The second one is the absence of zero point flux which is incompatible with the fact that vacuum energy to which magnetic energy contribute is not zero as predicted by particle physics theories and as observed experimentally by Casimar. The third problem is the magnetic permeability quantization which is not yet been quantized. Magnetic flux quantization in superconductors is predicted theoretically and verified experimentally. The theoretical foundation is based mainly on the fact that the current is zero which is in direct conflict with the fact that super current is observed experimentally to flow. The zero current make the conductivity finite which contradict the fact that the conductivity is infinite. The magnetic quantization in superconductors is not related to the magnetic quantum number. This does not agree with the fact that magnetic quantization on the atomic scale is related to the magnetic quantum number. The electric field quantization is not also well established. This manifests itself in the lack of full theoretical expression for Hall voltage quantization. In this thesis Schrödinger quantum mechanical equation based on harmonic oscillator, and particle in a box, beside Maxwell's electromagnetic equations quantizes magnetic permeability. It also quantizes flux without making the current vanishes, thus it agrees with the fact that super current is observed to flow. It also makes the conductivity infinite. The fact that model quantizes the magnetic permeability, conform with the fact that physical parameters should be quantized according to the laws of quantum mechanics. The fact that magnetic quantization exists for particle in a box opens a new IV horizon on quantizing magnetic field by producing isolated quantum nano particles. The magnetic flux quantization processes, the prediction of Zeeman effect energy and flux quantization with zero point background are compatible with the predictions of the existence of zero point background in quantum mechanics and the fact that vacuum energy is not zero. The quantization of electric field via the voltage which is related to the energy gap enables Hall voltage quantization. The model thus explains quantum Hall effect theoretically on a new basis which relies on harmonic oscillator model. The fact that harmonic oscillator model contribute to solving these problems, raises a hope that string theories, which are based on the fact that strings are harmonic oscillators, is a powerful theoretical tool which can solve many out standing physical problems.