On four-particle system ground state

1969 ◽  
Vol 63 (2) ◽  
pp. 593-610 ◽  
Author(s):  
V. S. Olkhovsky ◽  
E. Recami
Keyword(s):  
Ground State ◽  
Particle System ◽  
System 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.

HYPERSPHERICAL APPROACH TO STUDY THE SCHRÖDINGER EQUATION FOR AN N-PARTICLE SYSTEM

2009 ◽  
Vol 18 (07) ◽  
pp. 1497-1502
Author(s):  
H. HASSANABADI ◽  
A. A. RAJABI ◽  
M. M. SHOJAEI
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Excited States ◽  
Ground State ◽  
Schrodinger Equation ◽  
Particle System ◽  
Exact Analytical Solution ◽  
Hyperspherical Approach

In the present work we give an exact analytical solution of the Schrödinger equation for an N-particle system by using the hyperspherical approach, in the presence of the hypercentral potential of form V(R) = a1R2+b1R-4+c1R-6 for both the ground state and the excited states.

APPLICATION OF EIGENFUNCTIONAL THEORY ON QUANTUM MANY-PARTICLE SYSTEMS

2002 ◽  
Vol 16 (27) ◽  
pp. 4127-4163 ◽  
Author(s):  
YU-LIANG LIU
Keyword(s):  
Fixed Point ◽  
Hubbard Model ◽  
Green’S Function ◽  
Green's Function ◽  
Ground State ◽  
Particle System ◽  
Particle Systems ◽  
Fermion System ◽  
One Dimensional ◽  
Boson System

We first introduce the basic ingredients of the eigenfunctional theory, and show that a D-dimensional quantum many-particle system is mapped into a (D+1)-dimensional time-depending single-particle problem, and in the representation of the eigenfunctionals of the particle propagator, the particles become free. Then using this method, we study five kinds of quantum many-particle systems: interacting boson system, repulsive, attractive interacting fermion systems, Hubbard model and single-impurity scattering in one-dimensional fermion system, and demonstrate that the microscopic Bogoliubov theory and the phenomenological Bijl–Feynman theory of the bosons are closely related, and apart from an anti-symmetry factor Det ‖eikj·xl‖ the ground state wave function of the repulsive interacting fermion system has a similar form to that of the interacting boson system. Moreover, we show that the attractive interacting fermion system has a sound-type excitation spectrum like that in the interacting boson system. For one-dimensional Hubbard model we calculate the electron Green's function, and charge and spin density–density correlation functions which are consistent with the exact ones obtained by the Bethe ansatz and numerical calculations, and show that the ground state energy is increasing with U, and the electrons has single-occupied constraint in the large U limit. Finally, we demonstrate clearly the evolution of the system from its ultraviolet fixed point to infrared critical fixed point as the impurity potential increases. At the infrared critical fixed point, the fermion Green's function shows that the fermions are completely reflected on the impurity site.

The Effect of the Δ (1236)-Resonance in Nuclear Matter

1978 ◽  
Vol 33 (8) ◽  
pp. 861-886
Author(s):  
W. Manzke
Keyword(s):  
Schrödinger Equation ◽  
Nuclear Matter ◽  
Ground State ◽  
Schrodinger Equation ◽  
Particle System ◽  
Coupled System ◽  
Coupled Equations ◽  
Meson Theory ◽  
Partial Waves ◽  
The One

The effect of the resonant ⊿ (1236)-states in nuclear matter, is studied within the framework of the exp(S)-formalism [1, 2]. Treating the Schrödinger-Equation of the ground state of an A-particle fermion system with the help of the exp (S)-formalism one obtains a system of A coupled equations which all together are equivalent to the A particle Schrödinger equation. Neglecting three- and more particle forces as well as more particle effects the ground state of the A -particle system is described by the coupled system of one particle and two-particle-equations. Considering the special conditions of nuclear matter the one particle equations turn out to be trivial while the two particle equations reduce to a generalized Bethe-Goldstone-equation. After decomposition of these equations into partial waves we obtain a computable set of coupled integro-differential equations. These equations are fully selfconsistently solved including all partial waves up to total spin J = 2. Numerical calculation shows that the effects produced by ⊿-⊿-partial waves are comparable to those produced by N -⊿-partial waves. Transitions from the N-N channels to N-⊿ or ⊿-⊿ channels are caused by nonrelativistic potentials obtained from the static limit of meson theory. The N-N-interaction is described by a Reid-potential which is modified in order to reproduce the two particle dates (N-N phase shifts, deuteron).

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