scholarly journals Energy levels in muonic helium

2019 ◽  
Vol 222 ◽  
pp. 03009
Author(s):  
A.V. Eskin ◽  
V.I. Korobov ◽  
A.P. Martynenko ◽  
V.V. Sorokin
Keyword(s):  
Hyperfine Structure ◽  
Bound States ◽  
Energy Levels ◽  
Computer Code ◽  
Bound State ◽  
Relativistic Correction ◽  
Matrix Elements ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. As a result, numerical values of bound state energies and hyperfine structure are obtained. We calculate also correction to the structure of the nucleus, vacuum polarization and relativistic correction.

scholarly journals Hyperfine structure of muonic mesomolecules tdµ, tpµ, dpµ in variational method

2019 ◽  
Vol 222 ◽  
pp. 03011
Author(s):  
A.V. Eskin ◽  
V.I. Korobov ◽  
A.P. Martynenko ◽  
V.V. Sorokin
Keyword(s):  
Variational Method ◽  
Hyperfine Structure ◽  
Vacuum Polarization ◽  
Energy Levels ◽  
Computer Code ◽  
Wave Functions ◽  
Matrix Elements ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The hyperfine structure of energy levels of muonic molecules tdµ, tpµ and dpµ is calculated on the basis of stochastic variational method. The basis wave functions are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. Vacuum polarization, relativistic and nuclear structure corrections are taken into account to increase the accuracy. For numerical calculation, a computer code is written in the MATLAB system. Numerical values of energy levels of hyperfine structure in muonic molecules tdµ, tpµ and dpµ are obtained.

scholarly journals Bound states of dtμ, pdμ and t pμ mesomolecules

2019 ◽  
Vol 204 ◽  
pp. 05006 ◽  
Author(s):  
A. V. Eskin ◽  
V. I. Korobov ◽  
A. P. Martynenko ◽  
V. V. Sorokin
Keyword(s):  
Numerical Calculation ◽  
Bound States ◽  
Computer Code ◽  
Bound State ◽  
Wave Functions ◽  
Matrix Elements ◽  
Muonic Molecule ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of excited bound states of muonic molecules ptμ, pdμ, and dtμ is calculated on the basis of the stochastic variational method. The basis wave functions of the muonic molecule are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation, a computer code was written in the MATLAB system. As a result, the numerical values of bound state energies for excited P-states of muonic molecules ptμ, pdμ and dtμ were obtained.

1.37 - 2.90 Micron Intersubband Transitions in GaN/AlN Superlattices

2006 ◽  
Vol 955 ◽  
Author(s):  
Eric Anthony DeCuir ◽  
Emil Fred ◽  
Omar Manasreh ◽  
Jinqiao Xie ◽  
Hadis Morkoc ◽  
...  
Keyword(s):  
Quantum Wells ◽  
Bound States ◽  
Energy Levels ◽  
Three Dimensional ◽  
Blue Shift ◽  
Bound State ◽  
Peak Position ◽  
Multiple Quantum ◽  
Intersubband Transitions ◽  
Photovoltaic Mode

ABSTRACTIntersubband transitions in the spectral range of 1.37-2.90 °Cm is observed in molecular beam epitaxy grown Si-doped GaN/AlN multiple quantum wells using a Fourier-transform spectroscopy technique. A blue shift in the peak position of the intersubband transition is observed as the well width is decreased. A sample with a well width in the order of 2.4 nm exhibited the presence of three bound states in the GaN well. The bound state energy levels are calculated using a transfer matrix method. An electrochemical capacitance voltage technique is used to obtain the three dimensional carrier concentrations in these samples which further enable the calculation of the Fermi energy level position. Devices fabricated from these GaN/AlN quantum wells are found to operate in the photovoltaic mode.

scholarly journals ACCURACY OF APPROXIMATE EIGENSTATES

2000 ◽  
Vol 15 (20) ◽  
pp. 3221-3235 ◽  
Author(s):  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Eigenvalue Problem ◽  
Mass Spectra ◽  
Bound States ◽  
Main Tool ◽  
Bound State ◽  
Variational Techniques ◽  
The Matrix ◽  
Reasonable Choice ◽  
Unperturbed Solution ◽  
New Criteria

Besides perturbation theory, which requires the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum theory. For a reasonable choice of the employed trial subspace of the domain of H, the lowest eigenvalues of H can be located with acceptable precision whereas the trial-subspace vectors corresponding to these eigenvalues approximate, in general, the exact eigenstates of H with much less accuracy. Accordingly, various measures for the accuracy of approximate eigenstates derived by variational techniques are scrutinized. In particular, the matrix elements of the commutator of the operator H and (suitably chosen) different operators with respect to degenerate approximate eigenstates of H obtained by the variational methods are proposed as new criteria for the accuracy of variational eigenstates. These considerations are applied to that Hamiltonian the eigenvalue problem of which defines the spinless Salpeter equation. This bound-state wave equation may be regarded as the most straightforward relativistic generalization of the usual nonrelativistic Schrödinger formalism, and is frequently used to describe, e.g. spin-averaged mass spectra of bound states of quarks.

scholarly journals TOWARDS A THREE-DIMENSIONAL SOLUTION FOR 3N BOUND STATES WITH 3NFs

2009 ◽  
Vol 24 (11n13) ◽  
pp. 816-822 ◽  
Author(s):  
M. R. HADIZADEH ◽  
S. BAYEGAN
Keyword(s):  
Partial Wave ◽  
Integral Equations ◽  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Matrix Elements ◽  
Dimensional Solution ◽  
Dimensional Integral

After a brief discussion about the necessity of using the 3D approach, we present the non partial wave (PW) formalism for 3N bound state with the inclusion of 3N force (3NF). As an example the evaluation of 3NF matrix elements, which appear in the obtained coupled three-dimensional integral equations, for 2π-exchange Tucson–Melbourne 3NF show how would be this formalism efficient and less cumbersome in comparison with the PW formalism.

scholarly journals Quarkonium Production: Velocity-Scaling Rules and Long-Distance Matrix Elements

1997 ◽  
Vol 12 (22) ◽  
pp. 3951-3963 ◽  
Author(s):  
Gerhard A. Schuler
Keyword(s):  
Heavy Quark ◽  
Bound States ◽  
Potential Model ◽  
Distance Matrix ◽  
Bound State ◽  
Matrix Elements ◽  
Long Distance ◽  
Quarkonium Production ◽  
Quark Potential ◽  
Colour Octet

The hierarchy of long-distance matrix elements (MEs) for quarkonium production depends on their scaling with the velocity v of the heavy quark in the bound state. Ranges for the velocities in various bound states and uncertainties of colour-singlet MEs are estimated in a quark-potential model. Different possibilities for the scaling with v of the MEs are discussed; they depend on the actual values of v and the QCD scale. As an application, J/ψ polarization in e+e- annihilation is discussed. The first non-perturbative estimates of colour-octet MEs are presented and compared with phenomenological determinations. Finally, various predictions of prompt quarkonium production at LEP are compared.

scholarly journals Interação quadrupolar e sua correlação com o efeito Mössbauer

1982 ◽  
Vol 4 (4) ◽  
pp. 01
Author(s):  
Sylvestre Schneider
Keyword(s):  
Moment Tensor ◽  
Energy Levels ◽  
Multipole Expansion ◽  
Multipole Moment ◽  
Quadrupolar Interaction ◽  
Matrix Elements ◽  
Multipole Moments ◽  
Classical Charge ◽  
The Matrix ◽  
Mechanical Expression

By means multipole expansion, we guess the concept of "multipole moment". They are given examples of multipole moments. We start of them to define the "quadruploe moment tensor". By starting from the classical chargedents distribution of loads ρ (r-> ') and from the potencial expanded in a Taylor series, in which one one of the terms allows us to see the quadrupole moment, we construct a classical Hamiltonian in terms of quadrupole. The quantum-mechanical expression ĤQ por HQ is given, by substitution of the classical charge density ρ (r->) by an operator ρ (op), which describes adequately the real configuration in a non-continuous charge distribution. By use of the Clebsh-Gordan tecnology-coefficients with the irredutible tensors, the matrix-elements of ĤQ was calculated. The relation develloped, which allows the calcule of the matrix-elements of ĤQ, this is used for an application to a specific case, of a strong mafnetic field exerted on an atom. It is obtained a particular relation, for calculating the energy levels of quadrupolar interaction. The sequente purpose was to work out an application for an atom or ion in the fundamental staton 2S1/2, and nuclear spin 3/2 in a strong magnetic field.The results was a splitting in energy levels for the quadrupolar interaction. The quadrupolar interaction was examined in correlation of the Mössbauer-Effect in different examples.

Form Factors and Correlation Functions

2020 ◽  
pp. 744-788
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Correlation Functions ◽  
Form Factors ◽  
Vacuum Expectation ◽  
Bound State ◽  
Kernel Functions ◽  
Energy Tensor ◽  
Matrix Elements ◽  
Stress Energy ◽  
The Matrix ◽  
Recursive Equations

At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.

The Hydrogen Atom and Positronium

2019 ◽  
pp. 43-54
Author(s):  
Michael E. Peskin
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Hyperfine Structure ◽  
Energy Levels ◽  
Bound State ◽  
Electron Positron

This chapter discusses the physics of the hydrogen atom and the electron-positron bound state positronium. It describes the energy levels of these atoms, including the fine structure and hyperfine structure. It discusses the lifetimes of the two species of positronium.

Aharonov–Bohm effect in a Coulomb-type potential under the influence of a cutoff point

2021 ◽  
pp. 2150136
Author(s):  
K. Bakke
Keyword(s):  
Electric Fields ◽  
Bound States ◽  
Energy Levels ◽  
Bound State ◽  
Cutoff Point ◽  
Coulomb Type ◽  
Bohm Effect ◽  
Forbidden Region ◽  
Aharonov Bohm ◽  
Type Potential

We analyze the influence of a cutoff point on a Coulomb-type potential that stems from the interaction of an electron with electric fields. This cutoff point establishes a forbidden region for the electron. Then, we search for bound state solutions to the Schrödinger equation. In addition, we consider a rotating reference frame. We show that the effects of rotation break the degeneracy of the energy levels. Further, we discuss the Aharonov–Bohm effect for bound states.

Sign in / Sign up

Export Citation Format

Share Document