Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

2019 ◽  
Vol 119 (14) ◽  
pp. e25928 ◽  
Author(s):  
Jen‐Hao Ou ◽  
Yew Kam Ho
Keyword(s):  
Ground State ◽  
Wave Functions ◽  
Information Energy

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

The binding energies of atomic nuclei III. Nuclear forces and the ground state of oxygen 16

1959 ◽  
Vol 253 (1273) ◽  
pp. 186-198 ◽  
Keyword(s):  
Binding Energy ◽  
Electron Scattering ◽  
Ground State ◽  
Binding Energies ◽  
Wave Functions ◽  
Unperturbed System ◽  
Core Radius ◽  
Nuclear Forces ◽  
Potential Core ◽  
Atomic Nuclei

The r. m. s. radius and the binding energy of oxygen 16 are calculated for several different internueleon potentials. These potentials all fit the low-energy data for two nucleons, they have hard cores of differing radii, and they include the Gammel-Thaler potential (core radius 0·4 fermi). The calculated r. m. s. radii range from 1·5 f for a potential with core radius 0·2 f to 2·0 f for a core radius 0·6 f. The value obtained from electron scattering experiments is 2·65 f. The calculated binding energies range from 256 MeV for a core radius 0·2 f to 118 MeV for core 0·5 f. The experimental value of binding energy is 127·3 MeV. The 25% discrepancy in the calculated r. m. s. radius may be due to the limitations of harmonic oscillator wave functions used in the unperturbed system.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

Determination of hyperon properties through the variational method considering the hyperfine interaction

2019 ◽  
Vol 28 (10) ◽  
pp. 1950087 ◽  
Author(s):  
S. M. Moosavi Nejad ◽  
A. Armat
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Ground State ◽  
Radiative Decay ◽  
Magnetic Moments ◽  
Wave Functions ◽  
Decay Widths ◽  
Free Parameters ◽  
Theoretical Results

Performing a fit procedure on the hyperon masses, we first determine the free parameters in the Cornell-like hypercentral potential between the constituent quarks of hyperons in their ground state. To this end, using the variational principle, we apply the hyperspherical Hamiltonian including the Cornell-like hypercentral potential and the perturbation potentials due to the spin–spin, spin–isospin and isospin–isospin interactions between constituent quarks. In the following, we compute the hyperon magnetic moments as well as radiative decay widths of spin-3/2 hyperons using the spin-flavor wave function of hyperons. Our analysis shows acceptable consistencies between theoretical results and available experimental data. This leads to reliable wave functions for hyperons at their ground state.

TWO-ELECTRON SYSTEM IN THE FIELD OF GENERALIZED SCREENED POTENTIAL

2011 ◽  
Vol 25 (19) ◽  
pp. 1619-1629 ◽  
Author(s):  
ARIJIT GHOSHAL ◽  
Y. K. HO
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Electron System ◽  
Wave Functions ◽  
Expectation Values ◽  
Screening Parameter ◽  
System Ground State ◽  
Highly Correlated ◽  
First Time ◽  
Ground State Energies

Ground states of a two-electron system in generalized screened potential (GSP) with screening parameter λ: [Formula: see text] where ∊ is a constant, have been investigated. Employing highly correlated and extensive wave functions in Ritz's variational principle, we have been able to determine accurate ground state energies and wave functions of a two-electron system for different values of the screening parameter λ and the constant ∊. Convergence of the ground state energies with the increase of the number of terms in the wave function are shown. We also report various geometrical expectation values associated with the system, ground state energies of the corresponding one-electron system and the ionization potentials of the system. Such a calculation for the ground state of a two-electron system in GSP is carried out for first time in the literature.

Internal Rotation Spectrum in the Ground State of cis Propionyl Fluoride

1981 ◽  
Vol 36 (12) ◽  
pp. 1327-1333
Author(s):  
F. Scappini ◽  
H. Dreizler
Keyword(s):  
Internal Rotation ◽  
Ground State ◽  
Wave Functions ◽  
Rigid Rotor ◽  
Quantum Numbers ◽  
High K ◽  
Forbidden Transitions ◽  
Low K ◽  
Rotation Spectrum

AbstractThe microwave ground state spectrum of cis propionyl fluoride has been investigated expanding, with respect to a previous study, the range of the quantum numbers of the transitions, J up to 40 and K up to 18. At low K the spectrum resembles that of an asymmetric rigid rotor, except in a number of cases where the lines are split into A, E doublets. At intermediate and high K the mixing of the if-doublet rigid rotor wave functions makes forbidden transitions appear. The results of the analysis of the methyl top internal rotation ground state splittings are: V3 = 2350 ± 11 cal/mole, ≮ (i, a) = 32.7° ±2.0°, and Iα = 3.18 ± 0.03 uÅ2.

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