Laughlin's Wave Function and Angular Momentum

Shrivastava, Keshav N.

doi:10.1142/s0217979211058602

Cited by 5 publications

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“…We find that the size of the devices is often only a few nm and temperatures of measurements are quite low such as mK. Our theory explains all of the data correctly [7]- [21].…”

Section: Introductionsupporting

confidence: 52%

The Quantum Hall Effect: Interpretation of the Experimental Data

Shrivastava¹

2013

IJAPM

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Abstract-The theory of integers and fractions at which plateaus arise in the quantum Hall effect is explained. The experimental values are noted and explained by using the theory of angular momentum in quantum mechanics. The special treatment of spin introduced by this work eliminates the Lande's formula of g values and introduces a formula which is linear in the angular momentum variables, L, S and J. At high fields, the +S states are symmetric with the -S states so that when there is a plateau at + state there is also one at -S state. A lot of states require that the Landau levels are modified by this spin effect.Index Terms-Quantum Hall effect, modified Lande's formula, landau levels, symmetric spin effect. I. INTRODUCTIONThe preliminary experimental work on the detection of fractions and integers at which plateaus occur in the quantum Hall effect was done by von Klitzing, Dorda and Pepper [1] and by Tsui, Stormer and Gossard [2]. It was thought that the wave function of electrons should be two dimensional as the Laughlin's wave function is [3]. Anderson [4] and Schrieffer [5] thought that Laughlin's wave function will provide a prototype wave function which will form the basic theory of charge fractionalization. Whether the charge fractionalizes in the quantum Hall effect or not by electron correlations is a different question but we have found that all of the data can be explained on the basis of spin symmetry and the angular momentum and not by Laughlin's wave function. Hence, the charge fractionalization does not occur by Laughlin's correlations. Later work showed that Laughlin's wave function is a zero-energy ground state of a very unusual potential which is unlikely to occur in solids and hence will not be useful to interpret the experimental data. The Laughlin's potential cannot be transformed into a Coulomb potential. They never claimed that Laughlin's wave function is the ground state of Coulomb's potential. Simply, we find it convenient and have understanding of the Coulomb potential as a fundamental law of nature. It will be a great service to the physics community if we can prove the equivalence between our angular momentum theory and the Laughlin's theory. It seems that it will be very difficult to find such an equivalence if it exists at all. What is the Hall effect resistivity? We are able to explain the Hall effect without the need of a wave function [6]. That means that the wave functions are hydrogen type, made from Legendre's polynomials with suitable modifications. The Hall resistivity is a linear Manuscript received August 2, 2012; revised September 21, 2012 The author is with the University of Hyderabad, India, also University of Malaya, Kuala Lumpur, Malaysia. (e-mail: keshav1001@yahoo.com).function of magnetic field. In real systems it is found to have fractional values which require understanding. We find that the size of the devices is often only a few nm and temperatures of measurements are quite low such as mK. Our theory explains all of the data correctly [7]-[21]. II. ELEMENT...

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“…We find that the size of the devices is often only a few nm and temperatures of measurements are quite low such as mK. Our theory explains all of the data correctly [7]- [21].…”

Section: Introductionsupporting

confidence: 52%

The Quantum Hall Effect: Interpretation of the Experimental Data

Shrivastava¹

2013

IJAPM

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“…Therefore, there is a spin-charge effect, i.e., under high magnetic fields, the spin determines the charge the Lande's formula is replaced by a linear formula and Landau levels are modified [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Laughlin's wave function is not the interpretation of quantum Hall effect [25].…”

Section: H Spin-charge Lockingmentioning

confidence: 99%

Universal Introduction to the Quantum Hall Effect

Shrivastava¹

2013

IJAPM

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Abstract-TheHall effect is the generation of a current perpendicular to the direction of applied electric as well as applied magnetic field in a metal or a semiconductor. It is used to determine the concentration of electrons. The Quantum Hall effect has been discovered by von Klitzing in Germany and by Tsui, Stormer and Gossard in U.S.A. Robert Laughlin also in U.S.A. explained the quantization of Hall current by using "flux quantization" and introduced incompressibility to obtain fractional charge. We have developed the theory of the quantum Hall effect by using the theory of angular momentum. Our predicted fractions are in accord with those measured. Von Klitzing in 1985, and Tsui, Stormer and Laughlin in 1998 received the Nobel prize for their discoveries. In this lecture, we report a review of the subject as well as emphasize our explanation of the observed phenomena. We use spin to explain the fractional charge and hence we discover spin-charge coupling. We find a new way to quantize the flux and compare our explanation with other prize winning researches.Index Terms-Angular momentum, flux quantization, hall effect, modified landau levels, modified lande's g value formula.

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DFT calculation of vibrational frequencies of clusters in GaAs and the Raman spectra

Devi

Shrivastava

2012

Spectrochimica Acta Part A: Molecular and Biomolecular Spectros

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Laughlin's Wave Function and Angular Momentum

Cited by 5 publications

References 587 publications

The Quantum Hall Effect: Interpretation of the Experimental Data

The Quantum Hall Effect: Interpretation of the Experimental Data

Universal Introduction to the Quantum Hall Effect

DFT calculation of vibrational frequencies of clusters in GaAs and the Raman spectra

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