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Quantum theory with conjecture of fractional charge quantization, eigenfunctions for fractional charge quantization, fractional Fourier transform, Hermite function for fractional charge quantization, and eigenfunction for a twisted and twigged electron quanta is developed and applied to resistivity, dielectricity, giant magneto resistance, Hall effect and conductance. Our theoretical relationship for quantum measurements is in good conformity and in agreement with most of the experimental results. These relationships will pave a new approach to quantum physics for deciphering measurements on single quantum particles without destroying them. Our results are in agreement with 2012 Physics Nobel Prize winning Scientists, Serge Haroche and David J. Wineland.

Experimental results in quantum physics since last three decades brought significant changes in our under- standing. The discovery of quantum Hall effect in heteorostructure semiconductors results in the Nobel Prize winning award for the year 1987 to Von Klitzing [

Now, we witnessed again new exciting experimental results on individual quantum systems which led the Nobel Prize winning award in physics by Serge Haroche and David J. Wineland in the year 2012. We studied American Institute of Physics (AIP) reports of 2012 prize winning award and all relevant research papers [

The fractional Fourier transform (FRFT) of order

where

Equation (2) is consistent with other definitions of Hermite polynomials. Saleem Iqbal [

Equation (3) represents plane wave for a rotation vector alpha (discussed in [

We shall use Equations (1)-(3) and relation (4) to obtain interesting results for different cases of physics problems.

We know that the electrical resistivity is the inverse of conductivity. The electrical conductivity according to Drude Model (classical) is defined as:

where n is the number of charge carriers, e the charge of an electron,

where

determined from relative heights of Raman peaks. The helicon profile of an electron is due to spinning or gyroscopic motion. To our conjecture, the dual nature of a quantum particle is a metaphoric states, i.e., it simultaneously behaves as particle and quanta. The fractional quantized state of charge in the momentum space are the manifestations of gyroscopic constant,

Remember that the conductivity is different from conductance.

The mesoscopic fields in a cavity are the manifestations of quantum mechanical dipole moments (fractional charge quantization to a single electron or many electrons systems) due to either molecules, atoms, ions or even the charge, being a constant physical entity, of an electron in the momentum space while interacting with photons. To our conjecture the quantum mechanical dipole moment is a fractional charge quantization, i.e.,

whrer D is the displacement of charge either on an electron or in many electrons system,

where

The most attractive quantum electrodynamic potential of an electron or electron quanta (the interior of which is envisaged as a potential well and is defined by the strength of the quantum well)

where

The megnetoresistance in quantum Hall effect should depend on magnetic field when an electron (charge as a constant physical entity) is fractionally quantized with twisting and twigging of an electron quanta. This is why we are interested in quantum Hall effect on heteorostructure semiconductors by Von Klitzing [

field is fractionally quantized with a gap of quantum Hall resistance, i.e.,

standing, this resistance is a manifestation of twisting and twigging effects of an electron quanta. This is visible

in our Equations (9) and (10), with a gyroscopic constant,

types, one is longitudinal and the other is transverse. The longitudinal magnetoresistance is associated with magnetic field parallel to the current. The excitonic quantized Hall state at total Landau level filling factor is unity with longitudinal component vanishing and Hall component developing. The Lorentz force, in QHE, for a single electron, is

Changing

an electron wire or string,

electron and

where

quantum numbers, i.e.,

Using eigenfunction

where

be solved by considering

e is changed with

(17). After substitutions and simplifications, Equation (17) is changed in to quantum cyclotron frequency for each of sub-quanta on the lateral surface of electron wire, i.e.,

With resonance Raman Scattering in the fractional regime,

Quantum conductance was first experimentally observed by Wees et al. [

conductance did not increase continuously but rather in quantized steps of

When the electronic mean free path of a wire exceeds the wire length, the wire behaves like an electron wave guide. Each wave guide mode or channel (ballistic conductors) contributes an amount

where

effect of Ohemic resistance and dynamic resistances (capacitive reactance and inductive reactance) is called impedance. The inverse of the impedance is termed as admittance. To our opinion, the inverse of the quantum Hall resistance is quantum conductance thus Equation (19) is modified as

We consider the current density j equal to current I,. i.e.,

With our conjecture of fractional charge quantization, change e with

with

where

where

Formulas for quantum resistivity (Quantum conductivity) and quantum conductance are developed by using fractional Fourier transform. Formulas for quantum behaviour of dielectricity and giant magneto resistance are suggested by using fractional Fourier transform. Formulas for quantum Hall effect following the fractional electric field are suggested. Raman and resonance Raman spectroscopy are suggested for measuring diverse parameters pertaining to quantum behaviour of resistivity, dielectricity, GMR, Hall effect and conductance.

Saleem Iqbal,Farhana Sarwar,Syed Masood Raza,Syed Mohsin Raza,1 1, (2016) Applications of Quantum Physics on Resistivity, Dielectricity, Giant Magneto Resistance, Hall Effect and Conductance. World Journal of Condensed Matter Physics,06,95-102. doi: 10.4236/wjcmp.2016.62013