scholarly journals FOUR-PARTICLE ANYON EXCITON: BOSON APPROXIMATION

1995 ◽  
Vol 09 (02) ◽  
pp. 123-133 ◽  
Author(s):  
M. E. Portnoi ◽  
E. I. Rashba
Keyword(s):  
Angular Momentum ◽  
Electron Density ◽  
Ground State ◽  
Hypergeometric Functions ◽  
Energy Levels ◽  
Confluent Hypergeometric Functions ◽  
Full Symmetry ◽  
Hole Confinement ◽  
Boson Approximation

A theory of anyon excitons consisting of a valence hole and three quasielectrons with electric charges –e/3 is presented. A full symmetry classification of the k = 0 states is given, where k is the exciton momentum. The energy levels of these states are expressed by quadratures of confluent hypergeometric functions. It is shown that the angular momentum L of the exciton ground state depends on the distance between the electron and hole confinement planes and takes the values L = 3n, where n is an integer. With increasing k the electron density shows a spectacular splitting on bundles. At first a single anyon splits off of the two-anyon core, and finally all anyons become separated.

A group theoretical approach to the many nucleon problem

1971 ◽  
Vol 70 (3) ◽  
pp. 485-496 ◽  
Author(s):  
J. A. de Wet
Keyword(s):  
Angular Momentum ◽  
Theoretical Approach ◽  
Ground State ◽  
Mass Number ◽  
Energy Levels ◽  
Quantum Numbers ◽  
The Many ◽  
Special Case ◽  
Ground State Energies ◽  
Good Agreement

Representations of the four-dimensional unitary group U4 were considered long ago by Wigner(1)as a model for nuclear isobaric multiplets. However, the Hamiltonian did not include the components of isospin which together with the spin coordinates are known to label the nuclear states. In this paper we shall find representations characterized by the eigenvalues of angular momentum J, isospin T and parity π, and will find mass relations which give good agreement with the experimental energy levels of Li6 and Be8 labelled by the same quantum numbers. The representations found by Wigner give good results for the ground state energies, or masses, of all the nuclei up to a mass number of A = 110(2), and we shall derive Wigner's representations as a special case. In fact, unless these are satisfied it is impossible for particle-like representations of U4 to exist!

scholarly journals A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms

2018 ◽  
Vol 73 (5) ◽  
pp. 407-414 ◽  
Author(s):  
Tigran A. Ishkhanyan ◽  
Vladimir P. Krainov ◽  
Artur M. Ishkhanyan
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Energy Levels ◽  
Hermite Functions ◽  
Exact Equation ◽  
Square Root ◽  
Centrifugal Barrier ◽  
Confluent Hypergeometric Functions

AbstractWe present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term ~x−1/2 with arbitrary strength and a repulsive centrifugal barrier core ~x−2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrödinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels.

Extensions to the spark spectra of zinc. I. Zinc II and zinc IV

1968 ◽  
Vol 46 (10) ◽  
pp. 1241-1251 ◽  
Author(s):  
A. M. Crooker ◽  
K. A. Dick
Keyword(s):  
Energy Level ◽  
Ground State ◽  
Level Scheme ◽  
Energy Levels ◽  
Spectral Lines ◽  
Energy Level Scheme ◽  
New Energy ◽  
Ground State Doublet

The spectrum of Zn II has been extended to complete the configuration 3d94s(3D)4p′ and 3d94s(1D)4p″. The configurations 3d109f, 3d1010f, and 3d94s(3D)5s′ have been added and a number of levels of the configurations 3d94s(3D)4d′, 3d94s(1D)4d″, and 3d94s(3D)6s′ have been tentatively established. Our list of Zn II lines contains 363 classified lines.Improved wavelength measurements have necessitated a revision of our earlier report on the spectrum of Zn IV. All the energy levels have been shifted slightly with respect to the ground state doublet 3d92D. In addition, 3 of 17 even levels and 10 of 43 odd levels have been changed. The new energy-level scheme results in the classification of 329 spectral lines as compared with 200 lines in the previous report.

scholarly journals Environment of Er Doped in a-Si:H and Its Relation with Photoluminescence Spectra

2006 ◽  
Vol 910 ◽  
Author(s):  
Minoru Kumeda ◽  
Yoshitaka Sekizawa ◽  
Akiharu Morimoto ◽  
Tatsuo Shimizu
Keyword(s):  
Angular Momentum ◽  
Ground State ◽  
Photoluminescence Spectrum ◽  
Energy Levels ◽  
Field Potential ◽  
Photoluminescence Spectra ◽  
Stark Splitting ◽  
Oxygen Ions ◽  
Structural Fluctuation ◽  
Er Doped

AbstractThe crystal-field potential at the Er3+ ion surrounded by six oxygen ions is expanded in terms of polynomials. After converting it into equivalent angular momentum operators, the Stark-splitting of the 4I15/2 ground state of the Er3+ ion is calculated. Influence of the change in the environment of the Er3+ ion on the shift of the energy levels is investigated and compared with the observed Er photoluminescence spectrum in a-Si:H. The scattering of the calculated energy levels by the structural fluctuation around the Er3+ ion is also compared with the linewidth of the component photoluminescence lines.

scholarly journals Exact Solution of the Schrödinger Equation for Composition of Coulomb and Oscillator Potentials

2021 ◽  
Vol 24 (2) ◽  
pp. 203-206
Author(s):  
V. V. Kudryashov ◽  
A. V. Baran
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hypergeometric Functions ◽  
Continuous Solution ◽  
Energy Levels ◽  
Discrete Energy ◽  
Radial Wave ◽  
Confluent Hypergeometric Functions ◽  
Radial Schrödinger Equation ◽  
Boundary Distance

The spherically symmetric potential is considered whose dependence on the distance r is described by the smooth composition of Coulomb at r < r0 and oscillator at r > r0 potentials. The boundary distance r0 is determined by the parameters of these potentials. The exact continuous solution of the radial Schrödinger equation is expressed in terms of the confluent hypergeometric functions. The discrete energy levels are obtained. The graphic illustrations for the energy spectrum and the radial wave functions are presented.

scholarly journals Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Quantum Interference ◽  
Direct Detection ◽  
Energy Levels ◽  
Vacuum Fluctuations ◽  
Heavy Particles ◽  
Evolving Systems ◽  
Gedanken Experiment ◽  
Classical Computer

AbstractFast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment.

THE ANGULAR MOMENTUM DEPENDENT CALCULATION OF THE GROUND STATE ENERGY OF LIQUID 3He

2005 ◽  
Vol 19 (30) ◽  
pp. 1793-1802 ◽  
Author(s):  
M. MODARRES
Keyword(s):  
Angular Momentum ◽  
Ground State Energy ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
Interatomic Potentials ◽  
Channel Correlation ◽  
P Waves ◽  
Effective Interactions ◽  
Three Body

We investigate the possible angular momentum, l, dependence of the ground state energy of normal liquid 3 He . The method of lowest order constrained variational (LOCV) which includes the three-body cluster energy and normalization constraint (LOCVE) is used with angular momentum dependent two-body correlation functions. A functional minimization is performed with respect to each l-channel correlation function. It is shown that this dependence increases the binding energy of liquid 3 He by 8% with respect to calculations without angular momentum dependent correlation functions. The l=0 state has completely different behavior with respect to other l-channels. It is also found that the main contribution from potential energy comes from the l=1 state (p-waves) and the effect of l≥11 is less than about 0.1%. The effective interactions and two-body correlations in different channels are being discussed. Finally we conclude that this l-dependence can be verified experimentally by looking into the magnetization properties of liquid helium 3 and interatomic potentials.

scholarly journals On the birthday problem: some generalizations and applications

2003 ◽  
Vol 2003 (60) ◽  
pp. 3827-3840 ◽  
Author(s):  
P. N. Rathie ◽  
P. Zörnig
Keyword(s):  
Probability Distribution ◽  
Random Graph ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Exact Probability ◽  
Confluent Hypergeometric Functions ◽  
Birthday Problem ◽  
Exact Probability Distribution

We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functionsU(−;−;−)which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.

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