### 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.