Analysis of the Three Parameter Wave Function of Hylleraas for the He i Ground State in Terms of Central Field Wave Functions

1954 ◽  
Vol 96 (2) ◽  
pp. 319-325 ◽  
Author(s):  
Louis C. Green ◽  
Marjorie M. Mulder ◽  
Paul C. Milner ◽  
Margaret N. Lewis ◽  
John W. Woll ◽  
...  
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Wave Functions ◽  
Central Field ◽  
Field Wave ◽  
Parameter Wave

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.

Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

2015 ◽  
Vol 70 (7) ◽  
pp. 499-505 ◽  
Author(s):  
Zahra Sharifi ◽  
Fateme Tajic ◽  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Wave Function ◽  
Magnetic Fields ◽  
Ground State ◽  
Bound States ◽  
State Energy ◽  
Potential Model ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Ansatz Method

AbstractThe Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

Exact solutions to solitonic profile mass Schrödinger problem with a modified Pöschl–Teller potential

2016 ◽  
Vol 31 (04) ◽  
pp. 1650017 ◽  
Author(s):  
Shishan Dong ◽  
Qin Fang ◽  
B. J. Falaye ◽  
Guo-Hua Sun ◽  
C. Yáñez-Márquez ◽  
...  
Keyword(s):  
Wave Function ◽  
Exact Solutions ◽  
Ground State ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Numerical Calculations ◽  
Potential Parameter ◽  
Heun Functions ◽  
Single Well

We present exact solutions of solitonic profile mass Schrödinger equation with a modified Pöschl–Teller potential. We find that the solutions can be expressed analytically in terms of confluent Heun functions. However, the energy levels are not analytically obtainable except via numerical calculations. The properties of the wave functions, which depend on the values of potential parameter [Formula: see text] are illustrated graphically. We find that the potential changes from single well to a double well when parameter [Formula: see text] changes from minus to positive. Initially, the crest of wave function for the ground state diminishes gradually with increasing [Formula: see text] and then becomes negative. We notice that the parities of the wave functions for [Formula: see text] also change.

Electronic wave functions II. A calculation for the ground state of the beryllium atom

1950 ◽  
Vol 201 (1064) ◽  
pp. 125-137 ◽  
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
Accurate Result ◽  
Energy Criterion ◽  
Wave Functions ◽  
Exponential Functions ◽  
Approximate Wave Function ◽  
Electronic Wave Functions ◽  
Approximate Wave

An approximate wave function expressed in terms of exponential functions, spherical harmonics, etc., with numerical coefficients has been calculated for the ground state of the beryllium atom . Judged by the energy criterion this gives a more accurate result than the Hartree result which was the best previously known. This has been calculated as a trial of a fresh method of calculating atomic wave functions. A linear combination of Slater determinants is treated by the variational method. The results suggest that this will provide a more powerful and convenient method than has previously been available for atoms with more than two electrons.

Ground-State Wave Functions for He i andH−Obtained by the Superposition of Central Field Functions

1956 ◽  
Vol 104 (6) ◽  
pp. 1593-1595 ◽  
Author(s):  
Louis C. Green ◽  
Carolyn D. Chandler ◽  
Patricia P. Rush
Keyword(s):  
Ground State ◽  
Wave Functions ◽  
Central Field ◽  
State Wave

On the theory of elastic collisions between electrons and hydrogen atoms

1960 ◽  
Vol 254 (1277) ◽  
pp. 259-272 ◽  
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Boundary Conditions ◽  
Continuous Spectrum ◽  
Ground State ◽  
Wave Functions ◽  
Hydrogen Atoms ◽  
Complete Set ◽  
Exchange Scattering ◽  
Conditions At Infinity

A hydrogen atom in the ground state scatters an electron with kinetic energy too small for inelastic collisions to occur. The wave function Ψ(r 1 ; r 2 ) of the system has boundary conditions at infinity which must be chosen to allow correctly for the possibilities of both direct and exchange scattering. The expansion Ψ = Σ ψ,(r 1 )F y (r 2 ) of the total wave function in y terms of a complete set of hydrogen atom wave functions ψ y (r 1 ) includes an integration over the continuous spectrum. It is si own that the integrand contains a singularity. The explicit form of this singularity and its connexion with the boundary conditions are examined in detail. The symmetrized functions Y* may be represented by expansions of the form Σ {ψ y (r 1 ) G y ±(r 2 ) ±ψ y (r 2 ) y G y ±(r 1 )}, where the integrand in the continuous spectrum does not involve singularities. Finally, it is shown that because all the states ψ y of the hydrogen atom are included in the expansion, the equation satisfied by F 1 , the coefficient of the ground state, contains a polarization potential which behaves like — a/2 r 4 for large r and is independent of the velocity of the incident electron.

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