scholarly journals The energy level shifts, wave functions and the probability current distributions for the bound scalar and spinor particles moving in a uniform magnetic field

2011 ◽  
Vol 42 (6) ◽  
pp. 895-910
Author(s):  
V. N. Rodionov ◽  
G. A. Kravtsova
Keyword(s):  
Magnetic Field ◽  
Energy Level ◽  
Uniform Magnetic Field ◽  
Wave Functions ◽  
Probability Current ◽  
Current Distributions ◽  
Level Shifts

ENERGY LEVEL OF ELECTRON IN AN ANISOTROPIC QUANTUM DOT UNDER A MAGNETIC FIELD BY AN INVARIANT EIGENOPERATOR METHOD

2006 ◽  
Vol 20 (32) ◽  
pp. 5417-5425
Author(s):  
HONG-YI FAN ◽  
TONG-TONG WANG ◽  
YAN-LI YANG
Keyword(s):  
Magnetic Field ◽  
Energy Level ◽  
Quantum Dot ◽  
Harmonic Oscillator ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Isotropic Harmonic Oscillator ◽  
Anisotropic Quantum Dot

We show that the recently proposed invariant eigenoperator method can be successfully applied to solving energy levels of electron in an anisotropic quantum dot in the presence of a uniform magnetic field (UMF). The result reduces to the energy level of electron in isotropic harmonic oscillator potential and in UMF naturally. The Landau diamagnetism decreases due to the existence of the anisotropic harmonic potential.

Proton Wave Functions in a Uniform Magnetic Field

2011 ◽  
Author(s):  
Dale S. Roberts ◽  
Patrick O. Bowman ◽  
Waseem Kamleh ◽  
Derek B. Leinweber
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Wave Functions

scholarly journals 2D relativistic oscillators with a uniform magnetic field in anti-de Sitter space

2021 ◽  
pp. 2150113
Author(s):  
Lakhdar Sek ◽  
Mokhtar Falek ◽  
Mustafa Moumni
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Principal Quantum Number ◽  
Wave Functions ◽  
De Sitter ◽  
Energy Eigenvalues ◽  
Space Deformation ◽  
Klein Gordon ◽  
Sitter Model ◽  
De Sitter Model

We study analytically the two-dimensional deformed bosonic oscillator equation for charged particles (both spin 0 and spin 1 particles) subject to the effect of an uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the anti-de Sitter model and we use the Nikiforov–Uvarov (NU) method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein–Gordon and scalar Duffin–Kemmer–Petiau (DKP) cases and we find that the deformed spectrum remains discrete even for large values of the principal quantum number. For spin 1 DKP case, we deduce the behavior of the DKP equation and write the nonrelativistic energies and we show that the space deformation adds a new spin-orbit interaction proportional to its parameter. Finally, we study the thermodynamic properties of the system and here we find that the effects of the deformation on the statistical properties are important only in the high-temperature regime.

A REALIZATION OF DYNAMIC GROUP FOR AN ELECTRON IN A UNIFORM MAGNETIC FIELD

2002 ◽  
Vol 11 (04) ◽  
pp. 265-271 ◽  
Author(s):  
SHISHAN DONG ◽  
SHI-HAI DONG
Keyword(s):  
Magnetic Field ◽  
Relativistic Electron ◽  
Uniform Magnetic Field ◽  
Wave Functions ◽  
Matrix Elements ◽  
Eigenvalues And Eigenfunctions ◽  
Radial Wave ◽  
Creation And Annihilation Operators ◽  
The Matrix ◽  
Analytical Expressions

The eigenvalues and eigenfunctions of the Schrödinger equation with a non-relativistic electron in a uniform magnetic field are presented. A realization of the creation and annihilation operators for the radial wave-functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions ρ2 and [Formula: see text].

Squeezing Transformation for Dynamics of An Electron in Uniform Magnetic Field and a Harmonic Potential

1997 ◽  
Vol 11 (06) ◽  
pp. 239-244 ◽  
Author(s):  
Hong-Yi Fan ◽  
Yan Zhang
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Uniform Magnetic Field ◽  
Cyclotron Frequency ◽  
Quantum Hall ◽  
Wave Functions ◽  
Harmonic Potential

By virtue of the <λ| representation (Hong-yi Fan and Yong Ren, Mod. Phys. Lett.B10, 523 (1996)), which is useful for studying quantum Hall effect, we reveal that a squeezing mechanism directly corresponding to the variation of electron's cyclotron frequency is involved in the dynamics of an electron in a uniform magnetic field and a harmonic potential. Electron's wave functions are also derived by the squeezing transformation in the <λ| representation.

A USEFUL REPRESENTATION FOR STUDYING QUANTUM HALL EFFECT

1996 ◽  
Vol 10 (12) ◽  
pp. 523-529 ◽  
Author(s):  
HONG-YI FAN ◽  
YONG REN
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Uniform Magnetic Field ◽  
Quantum Hall ◽  
Algebraic Approach ◽  
Wave Functions

We show that the complete and orthonormal representation 〈λ|, which is constructed in terms of guiding centers and canonical momenta for describing the coordinate of an electron in a uniform magnetic field, provides us with a direct algebraic approach to deriving the correct wave functions for studying quantum Hall effect. The squeezing transformation for electron’s motion radius in the 〈λ| representation is also discussed, normally ordered squeezing operators are derived by virtue of the technique of integration within an ordered product of operators.

Single-particle currents in the cranked harmonic oscillator model

1982 ◽  
Vol 60 (6) ◽  
pp. 809-814 ◽  
Author(s):  
M. A. Z. Habeeb ◽  
A. R. K. Aziz
Keyword(s):  
Harmonic Oscillator ◽  
Single Particle ◽  
Wave Functions ◽  
Oscillator Model ◽  
Coordinate Space ◽  
First Order ◽  
Probability Current ◽  
Current Distributions ◽  
Harmonic Oscillator Model ◽  
Angular Velocities

Using exact wave functions of the cranked triaxial harmonic oscillator model in coordinate space, an expression for the single-particle probability current density is derived. This expression, valid to all orders in the angular velocity is then used to calculate current distributions for some typical harmonic oscillator single-particle states. Comparisons with perturbative first-order calculations indicate differences at high angular velocities where new features of the current distributions become apparent. This suggests the extension of the present calculations to real nuclei.

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