scholarly journals RESONANCES FOR A HYDROGENIC SYSTEM OR A HARMONIC OSCILLATOR STRONGLY COUPLED TO A FIELD

2008 ◽  
Vol 23 (20) ◽  
pp. 3095-3112 ◽  
Author(s):  
CLAUDE BILLIONNET
Keyword(s):  
Harmonic Oscillator ◽  
Energy Levels ◽  
Stable States ◽  
Strongly Coupled ◽  
Energy Lowering ◽  
Massless Boson

We calculate resonances which are formed by a particle in a potential which is either Coulombian or quadratic when the particle is strongly coupled to a massless boson, taking only two energy levels into consideration. From these calculations we derive how the moving away of the particle from its attraction center goes together with the energy lowering of hybrid states that this particle forms with the field. We study the width of these states and we show that stable states may also appear in the coupling.

scholarly journals Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Luke Gayer ◽  
Nicolas Lang ◽  
Sinéad M. Ryan ◽  
David Tims ◽  
Christopher E. Thomas ◽  
...  
Keyword(s):  
Scattering Amplitudes ◽  
Lattice Qcd ◽  
Quark Mass ◽  
Light Quark ◽  
Energy Levels ◽  
Experimental Result ◽  
Infinite Volume ◽  
Resonance Pole ◽  
Strongly Coupled ◽  
Light Quark Mass

Abstract Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a $$ {D}_0^{\ast } $$ D 0 ∗ resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , and $$ {D}_0^{\ast } $$ D 0 ∗ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $$ {D}_0^{\ast } $$ D 0 ∗ is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , in contrast to the currently reported experimental result.

The spectroscopy of van der Waals molecules

1976 ◽  
Vol 54 (5) ◽  
pp. 487-504 ◽  
Author(s):  
George E. Ewing
Keyword(s):  
Energy Levels ◽  
Van Der Waals ◽  
Electronic Spectroscopy ◽  
Spectroscopic Constants ◽  
Intermolecular Potential ◽  
Interatomic Potentials ◽  
Strongly Coupled ◽  
Van Der Waals Molecules ◽  
Angular Momenta ◽  
Vibration Rotation

The recent spectroscopy of van der Waals molecules is reviewed. Examples are presented from radio-frequency, microwave, Raman, infrared, and electronic spectroscopy. Diatomic van der Waals molecules (e.g. Ne2, Ar2, Kr2, Mg2) reveal a manifold of closely spaced vibration–rotation levels consistent with the small dissociation energies which are orders of magnitude less than for ordinary chemically bonded molecules. The (isotropic) interatomic potentials which define these molecules may be evaluated from their energy levels. Polyatomic van der Waals molecules (e.g. H2–Ar, FCl–Ar, (H2)2, (O2)2, (CO2)2) are classified according to the strength of the (anisotropic) intermolecular potential which tends to define their geometry. This classification depends on the nature of the coupling of the rotational angular momenta and leads to a labeling of the complexes as free rotor, weakly coupled, strongly coupled, or semirigid. The spectroscopic constants which are determined from the energy levels of diatomic and polyatomic van der Waals molecules can be used to better understand the intermolecular bonding which holds these molecules together.

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 MARINARI–PARISI AND SUPERSYMMETRIC COLLECTIVE FIELD THEORY

1993 ◽  
Vol 08 (15) ◽  
pp. 2517-2550 ◽  
Author(s):  
JOÃO P. RODRIGUES ◽  
ANDRÉ J. VAN TONDER
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Harmonic Oscillator ◽  
String Field Theory ◽  
Continuum Limit ◽  
Infinite Sequence ◽  
Majorana Fermion ◽  
Oscillator Basis ◽  
Continuum Description ◽  
Massless Boson

A field theoretic formulation of the Marinari–Parisi supersymmetric matrix model is established and shown to be equivalent to a recently proposed supersymmetrization of the bosonic collective string field theory. It also corresponds to a continuum description of super-Calogero models. The perturbation theory of the model is developed and, in this approach, an infinite sequence of vertices is generated. A class of potentials is identified for which the spectrum is that of a massless boson and Majorana fermion. For the harmonic oscillator case, the cubic vertices are obtained in an oscillator basis. For a rather general class of potentials it is argued that one cannot generate from Marinari–Parisi models a continuum limit similar to that of the d = 1 bosonic string.

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>

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