Higher energy levels of the harmonic oscillator and stochastic electrodynamics

1975 ◽  
Vol 14 (3) ◽  
pp. 207-210 ◽  
Author(s):  
M. Surdin
Keyword(s):  
Harmonic Oscillator ◽  
Energy Levels ◽  
Stochastic Electrodynamics

scholarly journals Geometric Models of the Relativistic Harmonic Oscillator

1997 ◽  
Vol 12 (20) ◽  
pp. 3545-3550 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Harmonic Oscillator ◽  
Finite Number ◽  
Continuous Spectrum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Energy Spectra ◽  
De Sitter ◽  
Geometric Models ◽  
Relativistic Harmonic Oscillator ◽  
Quantum Models

A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1 + 1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.

scholarly journals THE q-DEFORMED SCHRÖDINGER EQUATION OF THE HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE

1994 ◽  
Vol 09 (22) ◽  
pp. 3989-4008 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA
Keyword(s):  
Euclidean Space ◽  
Difference Equation ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Series Representation ◽  
Exponential Functions ◽  
Creation And Annihilation Operators ◽  
The Creation

We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.

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 Analisis Energi Osilator Harmonik Menggunakan Metode Path Integral Hypergeometry dan Operator

2016 ◽  
Vol 2 (02) ◽  
pp. 7
Author(s):  
Fuzi Marati Sholihah ◽  
Suparmi S ◽  
Viska Inda Variani
Keyword(s):  
Energy Spectrum ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Integral Method ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Operator Method ◽  
One Dimensional ◽  
Equation Analysis ◽  
Path Integral Method

<span>Solution of the harmonic oscillator equation has a goal to get the energy levels of particles <span>moving harmonic. The energy spectrums of one dimensional harmonic oscillator are <span>analyzed by 3 methods: path integral, hypergeometry and operator. Analysis of the energy <span>spectrum by path integral method is examined with Schrodinger equation. Analysis of the <span>energy spectrum by operator method is examined by Hamiltonian in operator. Analysis of <span>harmonic oscillator energy by 3 methods: path integral, hypergeometry and operator are <span>getting same results 𝐸 = ℏ𝜔 (𝑛 + <span>1 2<span>)</span></span></span></span></span></span><br /></span></span></span>

scholarly journals Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 59 ◽  
Author(s):  
Theodorus Maria Nieuwenhuizen
Keyword(s):  
Harmonic Oscillator ◽  
Ground State ◽  
Average Rate ◽  
Average Energy ◽  
Initial Time ◽  
Stochastic Electrodynamics ◽  
Stochastic Force ◽  
Resonance Effects ◽  
Specific Position ◽  
Exact Shape

In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated by resonance effects only and results are derived that stem from those in the quantum ground state. For an orbit with specific position and momentum at an initial time, the average energy and the average rate of energy change are evaluated, which stem with each other. Resonance effects are highlighted along the way. An outlook on the hydrogen ground state problem is provided.

EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS

2007 ◽  
Vol 16 (01) ◽  
pp. 189-198 ◽  
Author(s):  
SHI-HAI DONG ◽  
D. MORALES ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Harmonic Oscillator ◽  
Analytical Solutions ◽  
Bound States ◽  
Energy Levels ◽  
Present Approach ◽  
Three Dimensions ◽  
One Dimension ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Pseudoharmonic Oscillator

By using the exact quantization rule, we present analytical solutions of the Schrödinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.

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