Energy Levels in a Bounded Isotropic Harmonic Oscillator Potential and Nuclear Shell Structure

1959 ◽  
Vol 115 (6) ◽  
pp. 1681-1682 ◽  
Author(s):  
S. Sengupta ◽  
S. Ghosh
Keyword(s):  
Harmonic Oscillator ◽  
Shell Structure ◽  
Energy Levels ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Isotropic Harmonic Oscillator ◽  
Nuclear Shell

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.

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.

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.

scholarly journals Do equidistant energy levels necessitate a harmonic potential?

2021 ◽  
Vol 53 (7) ◽  
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

AbstractExperimental 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 nth order 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 Nonrelativistic Atomic Spectrum for Companied Harmonic Oscillator Potential and its Inverse in both NC-2D: RSP

2015 ◽  
Vol 56 ◽  
pp. 1-9 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Harmonic Oscillator ◽  
Real Space ◽  
Gauge Condition ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Quadratic Potential ◽  
Shift Method ◽  
Exact Solvability ◽  
Isotropic Harmonic Oscillator ◽  
Standard Perturbation Theory

A novel study for the exact solvability of nonrelativistic quantum spectrum systems for companied Harmonic oscillator potential and its inverse (the isotropic harmonic oscillator plus inverse quadratic potential) is discussed used both Boopp’s shift method and standard perturbation theory in both noncommutativity two dimensional real space and phase (NC-2D: RSP), furthermore the exact corrections for the spectrum of studied potential was depended on two infinitesimals parameters θ and θ¯ which plays an opposite rolls, this permits us to introduce a new fixing gauge condition and we have also found the corresponding noncommutative anisotropic Hamiltonian.

scholarly journals Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Bahar ◽  
F. Yasuk
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Oscillator Potential ◽  
Ansatz Method ◽  
Harmonic Oscillator Potential ◽  
Klein Gordon ◽  
Dependent Mass ◽  
Mass Dependent ◽  
Klein Gordon Equation

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

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