Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

理论物理通讯：英文版

A New Differential Formula About Product of Polynomials and Its Application in Multi-electron State Physics

Fan Fan, Hong-Yi

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state related to Laughlin wave function. The entangled state representation for describing electrons in uniform magnetic field is used.

Related papers

A New Differential Formula About Product of Polynomials and Its Application in Multi-electron State Physics

Fan Hong-Yi

We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ``related to Laughlin wave function". The entangled state representation for describing electrons in uniform magnetic field is used.

Communications in Theoretical Physics•Sep 1, 2006•0 citations

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

Hong-Yi Fan

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.

International Journal of Modern Physics B•Aug 30, 2004•4 citations

WEYL CORRESPONDENCE FORMALISM FOR DESCRIBING ELECTRON UNDER UNIFORM MAGNETIC FIELD STUDIED BY VIRTUE OF THE ENTANGLED STATE REPRESENTATION

Nanrun Zhou, Liyun Hu, Hong-Yi Fan

Based on the entangled state representation for describing electron's coordinates under uniform magnetic field, we establish a one-to-one correspondence between quantum Hamiltonian and its classical Weyl function through the introduction of Wigner operator. We also study some new important properties of Wigner function of electron's quantum states, such as its upper bound, and its relation with electron's wave function. These discussions demonstrate the beauty and elegance of the entangled state representation.

International Journal of Modern Physics B•Mar 30, 2011•0 citations

Multi-variable special polynomials using an operator ordering method

Xiang‐Guo Meng, Kai‐Cai Li, Ji‐Suo Wang +4 more

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.

Frontiers of Physics•Jul 7, 2020•38 citations

A new kind of special function and its application

Hong-Yi Fan, Zhi-Long Wan, Ze Wu +1 more

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials. Its application in deriving the normalization for some quantum optical states is presented.

Chinese Physics B•Sep 29, 2015•7 citations

A new kind of special function and its application

范洪义, M LONG, 吴泽 +1 more

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.

中国物理B：英文版•Jan 1, 2015•0 citations
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.
Based on the entangled state representation for describing electron's coordinates under uniform magnetic field, we establish a one-to-one correspondence between quantum Hamiltonian and its classical Weyl function through the introduction of Wigner operator. We also study some new important properties of Wigner function of electron's quantum states, such as its upper bound, and its relation with electron's wave function. These discussions demonstrate the beauty and elegance of the entangled state representation.
Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.