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.

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.

DYNAMICAL SUPERSYMMETRY AND SOLUTIONS FOR PAULI HAMILTONIANS

1993 ◽  
Vol 08 (09) ◽  
pp. 827-836 ◽  
Author(s):  
JEAN-GUY DEMERS
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Harmonic Oscillator ◽  
Point Particle ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Relative Coordinate ◽  
Charged Point

A charged point particle interacting with a vortex in 2+1 dimensions (or the relative coordinate of two anyons) possesses a dynamical so(2, 1) symmetry that can be exploited to solve for the case when an external harmonic oscillator potential is added. Moreover, if the particle carries spin 1/2, its interaction with the vortex exhibits a dynamical spl*(2, 1) supersymmetry, which can be imported to the cases where a harmonic oscillator or an external magnetic field is present. Using this supersymmetry, the corresponding Pauli Hamiltonians can be solved algebraically.

scholarly journals Do Equidistant Energy Levels Necessitate a Harmonic Potential?

2021 ◽  
Author(s):  
Fabian Teichert ◽  
Eduard Kuhn ◽  
Angela Thränhardt
Keyword(s):  
Harmonic Oscillator ◽  
Shift Operator ◽  
Energy Levels ◽  
Experimental Results ◽  
Finite Range ◽  
Operator Approach ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Polynomial Potentials

Abstract Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only yields energy levels in a finite range and with a nonzero uncertainty. Within this study we review isospectral potentials from the literature and investigate the applicability of the harmonic oscillator hypothesis to recent measurements. First, we describe experimental results from literature by a harmonic oscillator model, obtaining a realistic size and depth of the resulting quantum well. Second, we use the shift-operator approach to calculate anharmonic non-polynomial potentials producing (partly) equidistant spectra. We discuss different potential types and interpret the possible modeling applications. Finally, by applying n th o rder perturbation theory we show that exactly equidistant eigenenergies cannot be achieved by polynomial potentials, except by the harmonic oscillator potential. In summary, we aim to give an overview over which conclusions may be drawn from the experimental determination of energy levels and which may not.

scholarly journals Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

2015 ◽  
Vol 58 (1) ◽  
pp. 7-13
Author(s):  
Theodor-Felix Iacob ◽  
Marina Lute ◽  
Felix Iacob
Keyword(s):  
Approximate Solution ◽  
Power Series ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Additional Term ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Gaussian Potential

Abstract We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

Exploration of perturbed dyonic theories

2009 ◽  
Vol 87 (10) ◽  
pp. 1059-1064
Author(s):  
S. C. Joshi
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Weak Magnetic Field ◽  
Energy Levels ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
Spin Orbit Interaction ◽  
Degenerate States

By extending the study of dyonic harmonic oscillator and dyonium in the presence of an external magnetic field, the possibility of observation of dyons has been explored. The splitting in energy levels of dyonium under the influence of a weak magnetic field has been undertaken with inclusion of spin-orbit interaction, and it is observed that the energy level splits into nondegenerate as well doubly degenerate states. The effect of a strong magnetic field on dyonium has also been carried out by treating spin-orbit interaction as a perturbation, leading to interesting results.

scholarly journals The harmonic oscillator approximation to the density matrix

1979 ◽  
Vol 57 (11) ◽  
pp. 1990-1998 ◽  
Author(s):  
R. K. Bhaduri ◽  
L. F. Zaifman
Keyword(s):  
Density Matrix ◽  
Harmonic Oscillator ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Numerical Comparisons ◽  
Isotropic Harmonic Oscillator ◽  
Matrix Expansion ◽  
Harmonic Oscillator Approximation ◽  
Spherical Nuclei ◽  
Special Case

The density matrix expansion for a system of nucleons moving in an isotropic harmonic oscillator potential is derived. This series is assumed to be a good approximation for the angle averaged density matrix of spherical nuclei, and is summed under a certain approximation. The form proposed by Campi and Bouyssy is obtained in our model as a special case. Other alternative forms are proposed and numerical comparisons are made using the Skyrme-III force.

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