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 New possibilities of harmonic oscillator basis application for calculation of the ground state energy of a Coulomb non-identical three-particle system

2017 ◽  
Vol 57 (2) ◽  
Author(s):  
Algirdas Deveikis
Keyword(s):  
Harmonic Oscillator ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Particle System ◽  
Traditional Approach ◽  
Expansion Method ◽  
Particle Systems ◽  
Oscillator Basis ◽  
Oscillator Length

A new harmonic oscillator (HO) expansion method for calculation of the non-relativistic ground state energy of the Coulomb non-identical three-particle systems is presented. The HO expansion basis with different size parameters in the Jacobi coordinates instead of only one unique oscillator length parameter in the traditional treatment is introduced. This method is applied to calculate the ground state energy of a number of Coulomb three-particle systems for up to 28 excitation HO quanta. The obtained results suggest that the HO basis with different size parameters in the Jacobi coordinates could lead to significant increasing of the rate of convergence for the ground state energy than in the traditional approach.

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 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.

Sign in / Sign up

Export Citation Format

Share Document