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

Communications in Theoretical Physics

Phase Operator Theory for an Electron Moving in a Uniform Magnetic Field

Fan Hong‐Yi, Wang Yihua, Fan Yue

Published Jul 30, 1998• 1 citation
Publisher

Abstract

We show that the newly found complete and orthonormal representation , which is constructed in terms of guiding centers and canonical momenta of an electron moving in a uniform magnetic field, also helps us to establish a systematic phase operator theory. The unitary phase operator, interpreted as a quantity canonically conjugated to the electron angular momentum, manifestly exhibits in the representation its phase behavior. As a byproduct, the phase distribution function, in the correct sense of probability in quantum mechanics, can also be defined by the representation.

DOI
10.1088/0253-6102/30/1/125

Related papers

Angular Momentum Conserved Coherent State for an Electron in a Uniform Magnetic Field

Hong-Yi Fan, Hui Zou, Yue Fan

For an electron in the uniform magnetic field, we construct the angular momentum conserved coherent state || r 2 , l ⟩, based on which we establish a new complete and orthonormal ⟨⟨ l,r | representation, where l represents the angular momentum and r the electron's orbit radius. Squeezing of the state | l,r ⟩⟩ is examined.

Chinese Physics Letters•Oct 1, 1999•5 citations

Angular Momentum-Phase Coherent State for an Electron in Uniform Magnetic Field

Fan Hong-Yi, Fan Yue

Based on the newly constructed state | l , r ⟩⟩ [Fan et al. , Chin. Phys. Lett. 16(1999)706], where l is the angular momentum quantum number and r denotes the electron's orbit radius in a uniform magnetic field, we propose a new angular momentum-phase coherent state by introducing a new operator A . A and A † are annihilation and creation operators in the | l , r ⟩⟩ space, respectively. The coherent state is A 's eigenket and possesses non-orthonormal and overcomplete properties. It is constructed on the certain superposition of zero-angular momentum states along the radius direction.

Chinese Physics Letters•Feb 8, 2001•15 citations

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

Hong-Yi Fan

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.

Modern Physics Letters B•Jun 10, 2001•2 citations

MINIMUM UNCERTAINTY STATES FOR ANGULAR-MOMENTUM–PHASE UNCERTAINTY RELATION IN RADIUS–PHASE DESCRIPTION OF AN ELECTRON IN UNIFORM MAGNETIC FIELD

Hong-Yi Fan

Based on the |λ> representation and the radius–phase description of an electron's orbit track in a uniform magnetic field, we introduce the phase operator and derive the minimum uncertainty states for the angular-momentum–phase uncertainty relation. The derivation makes full use of the newly constructed |l, r> representation which is the common eigenvector of the angular momentum Lz and the radius operator (K- - iΠ+)(K+ + iΠ-).

Modern Physics Letters B•Apr 10, 2000•2 citations

NEW REPRESENTATION FOR DESCRIBING LOWERING AND ASCENDING OF AN ELECTRON'S ANGULAR MOMENTUM IN A UNIFORM MAGNETIC FIELD

Hong-Yi Fan, H. ZOU, Yue Fan

We construct a new quantum mechanical representation |l,r> for describing an electron's angular momentum in a uniform magnetic field, where l is the eigenvalue of the azimuthal angular momentum Lz and r is the orbit radius of the electron's motion. The ascending and lowering operators for |l,r>→|l± 1,r> are also obtained. Throughout our discussion the <λ| representation is fully employed (see Hong-Yi Fan and Yong Ren, Mod. Phys. Lett.B10, 523 (1996).

Modern Physics Letters B•Apr 10, 1999•5 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
We show that the newly found complete and orthonormal representation , which is constructed in terms of guiding centers and canonical momenta of an electron moving in a uniform magnetic field, also helps us to establish a systematic phase operator theory. The unitary phase operator, interpreted as a quantity canonically conjugated to the electron angular momentum, manifestly exhibits in the representation its phase behavior. As a byproduct, the phase distribution function, in the correct sense of probability in quantum mechanics, can also be defined by the representation.
Based on the newly constructed state | l , r ⟩⟩ [Fan et al. , Chin. Phys. Lett. 16(1999)706], where l is the angular momentum quantum number and r denotes the electron's orbit radius in a uniform magnetic field, we propose a new angular momentum-phase coherent state by introducing a new operator A . A and A † are annihilation and creation operators in the | l , r ⟩⟩ space, respectively. The coherent state is A 's eigenket and possesses non-orthonormal and overcomplete properties. It is constructed on the certain superposition of zero-angular momentum states along the radius direction.
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.