The anisotropic harmonic oscillator in a magnetic field

1972 ◽  
Vol 5 (1) ◽  
pp. 1-4 ◽  
Author(s):  
T. K. Rebane
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator

Brownian motion of a classical harmonic oscillator in a magnetic field

2008 ◽  
Vol 77 (5) ◽  
Author(s):  
J. I. Jiménez-Aquino ◽  
R. M. Velasco ◽  
F. J. Uribe
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Harmonic Oscillator

GROUND STATE OF N HARMONICALLY BOUND ANYONS IN A MAGNETIC FIELD

1992 ◽  
Vol 07 (38) ◽  
pp. 3593-3600
Author(s):  
R. CHITRA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Harmonic Oscillator ◽  
Ground State ◽  
Harmonic Frequency ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Thomas Fermi ◽  
Large N ◽  
The Magnetic Field

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

Three-dimensional harmonic oscillator in a magnetic field

1971 ◽  
Vol 14 (4) ◽  
pp. 492-495 ◽  
Author(s):  
I. M. Ternov ◽  
V. G. Bagrov ◽  
V. N. Zadorozhnyi
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Three Dimensional

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.

Damping behavior of a harmonic oscillator in self-induced magnetic field of a solenoid

2019 ◽  
Vol 54 (2) ◽  
pp. 023002
Author(s):  
K H Raveesha ◽  
S Suma ◽  
R Ranjitha ◽  
R Rakshitha
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Induced Magnetic Field ◽  
Damping Behavior

Adiabatic invariants

2020 ◽  
pp. 359-376
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Single Molecule ◽  
Uniform Magnetic Field ◽  
Adiabatic Approximation ◽  
Magnetic Trap ◽  
Simplified Model ◽  
Adiabatic Invariants ◽  
Mathematical Pendulum ◽  
Simple Systems

This chapter addresses the adiabatic invariant for a mathematical pendulum, a model of a “gas” consisting of a single molecule in a piston, adiabatic approximation, and a simplified model of an ion H2+. The chapter also discusses the connection between the volume and the pressure of a gas consisting of particles inside an elastic cube, the adiabatic invariants for a charged anisotropic harmonic oscillator in a uniform magnetic field, a magnetic trap, and the action and angle variables for the simple systems.

Canonical transformations

2020 ◽  
pp. 317-337
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Canonical Transformation ◽  
Hamiltonian Function ◽  
Harmonic Oscillators ◽  
Nonlinear Coupling ◽  
Canonical Transformations ◽  
Canonical Variables ◽  
Anharmonic Oscillations ◽  
The Given

This chapter addresses the canonical transformation defined by the given generating function, the rotation in the phase space as a canonical transformation, and themovement of the system as a canonical transformation. The chapter also discusses using the canonical transformations for solving the problems of the anharmonic oscillations and using the canonical transformation to diagonalize the Hamiltonian function of an anisotropic charged harmonic oscillator in a magnetic field. Finally, the chapter addresses the canonical variables which reduce the Hamiltonian function of the harmonic oscillator to zero and using them for consideration of the system of the harmonic oscillators with the weak nonlinear coupling.

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