Improved (1s)2 variational model for helium

Open Physics ◽  
2005 ◽  
Vol 3 (1) ◽  
pp. 1-7
Author(s):  
B. Reed
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Nuclear Charge ◽  
Variational Model ◽  
Variational Parameter ◽  
Effective Nuclear Charge ◽  
Upper Limit ◽  
Trial Wavefunction ◽  
Present Trial

AbstractThe ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e −γ(rA/a o)ne−γ(rB/a o)n. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 Eh (Eh=1 hartree) in comparison with the traditional (n=1) result of −2.84766 Eh. This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 Eh) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 Eh, the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).

scholarly journals Two-Parameter Harmonic Oscillator Expansion Method for Calculating Non-Relativistic Ground State Energy of Coulomb Three-Particle Systems with Two Identical Particles

2018 ◽  
Vol 173 ◽  
pp. 02006
Author(s):  
Algirdas Deveikis
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Traditional Approach ◽  
Coulomb Systems ◽  
Expansion Method ◽  
Variational Parameter ◽  
Oscillator Representation ◽  
Identical Particles ◽  
Oscillator Basis

The variational method in oscillator representation with individual parameters for each Jacobi coordinate is applied to the non-relativistic calculation of the ground state energy of a number of three-particle Coulomb systems, consisting of two identical particles and a different one. The accuracy and convergence rate of the calculations in the constructed oscillator basis are studied up to a total of 28 oscillator quanta. The results are compared with those of the traditional approach using only one such nonlinear variational parameter. The method with individual parameters for Jacobi coordinates is found to possess a number of advantages as compared to the traditional approach.

scholarly journals AB Initio Calculations for Helium-4 of Thermodynamic and Transport Properties of the Gas and the Ground State Energy of the Liquid

1972 ◽  
Vol 25 (6) ◽  
pp. 735 ◽  
Author(s):  
IK Snook ◽  
RO Watts
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Second Virial Coefficient ◽  
Energy Curve ◽  
Self Diffusion ◽  
The Monte Carlo Method ◽  
Trial Wavefunction ◽  
Temperature Liquid ◽  
Variation Procedure

A potential energy curve for the 4He diatom obtained from a perturbation theory solution of the Schr�dinger equation is used to calculate the viscosity, thermal conductivity, self-diffusion coefficient, and second virial coefficient of gaseous 4He. In addition, the ground state energy of the zero-temperature liquid is obtained by a variation procedure using a trial wavefunction in conjunction with the Monte Carlo method. The results are in good agreement with experiment.

An upper limit to ground state energy fluctuations in nuclear masses

2007 ◽  
Author(s):  
Jorge G. Hirsch ◽  
Víctor Velázquez ◽  
Alejandro Frank ◽  
José Barea ◽  
Piet Van Isacker ◽  
...  
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Upper Limit ◽  
Nuclear Masses

An upper limit of ground-state energy fluctuations in nuclear masses

2006 ◽  
Vol T125 ◽  
pp. 158-161
Author(s):  
Jorge G Hirsch ◽  
Víctor Velázquez ◽  
Alejandro Frank ◽  
José Barea ◽  
Piet Van Isacker ◽  
...  
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Upper Limit ◽  
Nuclear Masses

scholarly journals A Note About the Ground State of the Hydrogen Molecule

2007 ◽  
Vol 72 (2) ◽  
pp. 164-170 ◽  
Author(s):  
Alexander V. Turbiner ◽  
Nicolais L. Guevara
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Trial Function ◽  
Hydrogen Molecule ◽  
State Energy ◽  
Variational Parameter ◽  
Electronic Correlation ◽  
Correlation Term

A trial function is presented for the H2 molecule which provides the most accurate (the lowest) Bohr-Oppenheimer ground state energy among few-parametric trial functions (with ≤14 parameters). It includes the electronic correlation term in the form ~ exp (γr12) where γ is a variational parameter.

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy

POLARON IN A QUANTUM DOT UNDER AN ELECTRIC FIELD

2007 ◽  
Vol 21 (24) ◽  
pp. 1635-1642
Author(s):  
MIAN LIU ◽  
WENDONG MA ◽  
ZIJUN LI
Keyword(s):  
Quantum Dot ◽  
Electric Field ◽  
Field Intensity ◽  
Ground State Energy ◽  
Ground State ◽  
Electric Field Intensity ◽  
State Energy ◽  
Theoretical Study ◽  
The Moment ◽  
Transformation Methods

We conducted a theoretical study on the properties of a polaron with electron-LO phonon strong-coupling in a cylindrical quantum dot under an electric field using linear combination operator and unitary transformation methods. The changing relations between the ground state energy of the polaron in the quantum dot and the electric field intensity, restricted intensity, and cylindrical height were derived. The numerical results show that the polar of the quantum dot is enlarged with increasing restricted intensity and decreasing cylindrical height, and with cylindrical height at 0 ~ 5 nm , the polar of the quantum dot is strongest. The ground state energy decreases with increasing electric field intensity, and at the moment of just adding electric field, quantum polarization is strongest.

Effects of a scattering center on the ground-state energy of quantum-dot lithium

2017 ◽  
Vol 31 (07) ◽  
pp. 1750071
Author(s):  
Z. D. Vatansever ◽  
S. Sakiroglu ◽  
I. Sokmen
Keyword(s):  
Quantum Dot ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Electronic Charge ◽  
Strongly Correlated ◽  
Configuration Interaction Method ◽  
Charge Localization ◽  
Scattering Center ◽  
Spin Properties

In this paper, the effects of a repulsive scattering center on the ground-state energy and spin properties of a three-electron parabolic quantum dot are investigated theoretically by means of configuration interaction method. Phase transition from a weakly correlated regime to a strongly correlated regime is examined from several strengths and positions of Gaussian impurity. Numerical results reveal that the transition from spin-1/2 to spin-3/2 state depends strongly on the location of the impurity which accordingly states the controllability of the spin polarization. Moreover, broken circular symmetry results in more pronounced electronic charge localization.

scholarly journals Observables in inhomogeneous ground states at large global charge

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Simeon Hellerman ◽  
Nozomu Kobayashi ◽  
Shunsuke Maeda ◽  
Masataka Watanabe
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Point Function ◽  
Ground State Configuration ◽  
Charge Densities ◽  
Direct Extension ◽  
Fixed Set ◽  
State Configuration ◽  
Large Charge

Abstract As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model. In this work, we prove that for generic ratios of two charge densities, ρ1/ρ2, the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for ρ1/ρ2 ≪ 1. We also compute, at fixed set of charges, ρ1, ρ2, the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale (ρ1 + ρ2)3/2, as dictated by dimensional analysis and similarly to the case of the O(2) model. Unlike the case of the O(2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.

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