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

Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion.

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

Modern Physics Letters B ◽

10.1142/s0217984900000343 ◽

2000 ◽

Vol 14 (07n08) ◽

pp. 235-242 ◽

Cited By ~ 2

Author(s):

HONG-YI FAN

Keyword(s):

Magnetic Field ◽

Angular Momentum ◽

Uniform Magnetic Field ◽

Uncertainty Relation ◽

Phase Operator ◽

Common Eigenvector ◽

Minimum Uncertainty ◽

The Common ◽

Phase Uncertainty

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-).

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

Modern Physics Letters B ◽

10.1142/s0217984901001914 ◽

2001 ◽

Vol 15 (12n13) ◽

pp. 407-414 ◽

Cited By ~ 2

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.

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

International Journal of Modern Physics B ◽

10.1142/s0217979204026196 ◽

2004 ◽

Vol 18 (20n21) ◽

pp. 2771-2817 ◽

Cited By ~ 4

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.

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THE DENSITY MATRIX FOR AN ELECTRON CONFINED IN QUANTUM DOTS UNDER A UNIFORM MAGNETIC FIELD

International Journal of Modern Physics B ◽

10.1142/s0217979206034637 ◽

2006 ◽

Vol 20 (16) ◽

pp. 2295-2303

Author(s):

QIANJUN PANG

Keyword(s):

Magnetic Field ◽

Quantum Dots ◽

Angular Momentum ◽

Density Matrix ◽

Unitary Transformation ◽

Uniform Magnetic Field ◽

Thermal Average ◽

Reasonable Result ◽

Divergence Problem ◽

Physical Quantities

By using unitary transformation and representation theory of quantum mechanics, we obtain two forms of density matrix respectively in (x1, p2) and (x1, x2) representations for an electron, with an anisotropic effective mass, confined in quantum dots under a uniform magnetic field (UMF). We find that both forms of density matrix can play an implemental role in the thermodynamical calculation. But, in order to calculate thermal average of angular momentum in z direction for this system, the density matrix in (x1, p2) representations is a more convenient form. When the confinement to electron in quantum dots disappears, we encounter a divergence problem of thermal average for some physical quantities. However, in the calculation of the thermal average of Hamiltonian, these divergent quantities cancelled each other out. And we eventually obtain a reasonable result.

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

Modern Physics Letters B ◽

10.1142/s0217984999000336 ◽

1999 ◽

Vol 13 (08) ◽

pp. 249-254 ◽

Cited By ~ 5

Author(s):

HONG-YI FAN ◽

H. ZOU ◽

YUE FAN

Keyword(s):

Magnetic Field ◽

Angular Momentum ◽

Uniform Magnetic Field ◽

Quantum Mechanical ◽

Quantum Mechanical Representation ◽

Lowering Operators

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).

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QUASI-PROBABILITY DISTRIBUTION FOR LAUGHLIN STATE VECTORS

Modern Physics Letters B ◽

10.1142/s021798490100194x ◽

2001 ◽

Vol 15 (14) ◽

pp. 463-472 ◽

Cited By ~ 2

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.

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