QUASI-PROBABILITY DISTRIBUTION FOR LAUGHLIN STATE VECTORS

2001 ◽  
Vol 15 (14) ◽  
pp. 463-472 ◽  
Author(s):  
HONGYI FAN ◽  
JINGXIAN LIN
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Angular Momentum ◽  
Probability Distribution ◽  
Wigner Function ◽  
State Vector ◽  
Uniform Magnetic Field ◽  
Gauge Invariant ◽  
Wigner Operator ◽  
Laughlin Wave Function

Based on the gauge-invariant Wigner operator in <λ| representation (see Ref. 10), where the state |λ> can conveniently describe the motion of an electron in a uniform magnetic field, we provide an approach for identifying the corresponding state vector for Laughlin wave function and deriving the Wigner function (quasi-probability distribution) for the Laughlin state vector. The angular momentum-excited Laughlin state vectors are also obtained via <λ| representation.

ANGULAR MOMENTUM-PHASE WIGNER OPERATOR FOR DESCRIBING ELECTRONS IN UNIFORM MAGNETIC FIELDS

2001 ◽  
Vol 15 (12n13) ◽  
pp. 407-414 ◽  
Author(s):  
HONGYI FAN
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Magnetic Fields ◽  
Wigner Function ◽  
Uniform Magnetic Field ◽  
Marginal Distributions ◽  
Wigner Operator

By introducing the angular momentum-phase Wigner operator both in <λ| representation and <l,r| representation, which are respectively the eigenstates of position and angular momentum of an electron in a uniform magnetic field, we establish the angular momentum-phase Wigner function whose marginal distributions are physically meaningful.

ENTANGLED STATE REPRESENTATIONS FOR DESCRIBING 2-DIMENSIONAL ELECTRON SYSTEM IN UNIFORM MAGNETIC FIELD

2004 ◽  
Vol 18 (20n21) ◽  
pp. 2771-2817 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Angular Momentum ◽  
Uniform Magnetic Field ◽  
Electron System ◽  
Entangled State ◽  
Dimensional Electron System ◽  
Einstein Podolsky Rosen ◽  
Set Up ◽  
Laughlin Wave Function

We review how to rely on the quantum entanglement idea of Einstein–Podolsky–Rosen and the developed Dirac's symbolic method to set up two kinds of entangled state representations for describing the motion and states of an electron in uniform magnetic field. The entangled states can be employed for conveniently expressing Landau wave function and Laughlin wave function with a fresh look. We analyze the entanglement involved in electron's coordinates (or momenta) eigenstates, and in the angular momentum-orbit radius entangled state. Various applications of these two representations, such as in developing angular momentum theory, squeezing mechanism, Wigner function and tomography theory for this system are presented. Thus the present review systematically summarizes a distinct approach for tackling this physical system.

NEW REPRESENTATION FOR GAUGE-INVARIANT WIGNER OPERATOR OF AN ELECTRON IN A UNIFORM MAGNETIC FIELD

1998 ◽  
Vol 13 (33) ◽  
pp. 2679-2687 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHEN-SHAN YANG
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Uniform Magnetic Field ◽  
Magnetic Vector Potential ◽  
Wigner Functions ◽  
Magnetic Vector ◽  
Ladder Operators ◽  
Gauge Invariant ◽  
Wigner Operator ◽  
Normal Product

By using the technique of integration within an ordered product (IWOP) of operators, we derive the normal-product form of the gauge-invariant Wigner operator of an electron in a uniform magnetic field and its expression in the newly constructed |λ> representation. The virtue of working in the |λ> representation lies in the fact that it is expressed in terms of the ladder operators Π±, K±(see Eq. (10)), thus the magnetic vector potential can naturally be included. On these bases we can easily obtain Wigner functions of some important electron states.

scholarly journals Is the Angular Momentum of an Electron Conserved in a Uniform Magnetic Field?

2014 ◽  
Vol 113 (24) ◽  
Author(s):  
Colin R. Greenshields ◽  
Robert L. Stamps ◽  
Sonja Franke-Arnold ◽  
Stephen M. Barnett
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Uniform Magnetic Field

A nodal determination of the Hall conductance

1991 ◽  
Vol 433 (1889) ◽  
pp. 547-571
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Uniform Magnetic Field ◽  
Periodic Potential ◽  
Electronic States ◽  
Simple Method ◽  
Hall Conductance ◽  
Nodal Structure ◽  
Nodal Pattern

We investigate the nodal structure of the electronic states which arise in the case of a uniform magnetic field and a weak periodic potential. By making use of the continuous motion of these zeros as the K -value labelling the state is varied, we introduce a simple method of obtaining the quantized value of the Hall conductance of a filled band from the nodal pattern of the band wave function. This method is demonstrated to give the correct results in the cases where the Hall conductances are known, given by the solutions of a Diophantine equation.

Wave Mechanics

2019 ◽  
pp. 91-174
Author(s):  
P.J.E. Peebles
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Angular Momentum ◽  
Hydrogen Atom ◽  
Physical System ◽  
Adjoint Operator ◽  
Physical Application ◽  
Wave Mechanics ◽  
Definite Form ◽  
Quantum Wave

This chapter develops the wave mechanics formalism. The emphasis here is on symmetries and conservation laws: parity, linear and angular momentum, and the electromagnetic interaction. The only specific physical application is the completion of the study of an isolated hydrogen atom, with some discussion of the motion of a particle in a magnetic field. The chapter also outlines the general assumptions of quantum wave mechanics, which may be summarized as follows: the state of a physical system is represented by a wave function and each measurable attribute of the system is represented by a linear self-adjoint operator in the space of functions. To apply these general assumptions to a given physical system, one must give a specific prescription for the observables and their algebra, and one must adopt a definite form for the Hamiltonians as a function of the observables.

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