scholarly journals Cluster Expansion of the Ground State of a Bose Particle System

1958 ◽  
Vol 19 (5) ◽  
pp. 595-597 ◽  
Author(s):  
Fumiaki Iwamoto
Keyword(s):  
Cluster Expansion ◽  
Ground State ◽  
Particle System

Cluster expansion of the wavefunction. Potential energy curves of the ground, excited, and ionized states of Li2

1985 ◽  
Vol 63 (7) ◽  
pp. 1857-1863 ◽  
Author(s):  
H. Nakatsuji ◽  
J. Ushio ◽  
T. Yonezawa
Keyword(s):  
Experimental Data ◽  
Potential Energy ◽  
Cluster Expansion ◽  
Ground State ◽  
Spectroscopic Properties ◽  
Bound State ◽  
Potential Energy Curves ◽  
Interaction Theory ◽  
Theoretical Results ◽  
S States

The SAC (symmetry-adapted-cluster) and SAC-CI theories based on the cluster expansion of the wavefunction have been applied to the calculations of the potential energy curves of the ground, excited, and ionized states of the Li2 molecule. The potential energy curves and the spectroscopic properties calculated agree well with the available experimental data and the previous theoretical results of Olson and Konowalow. For the [Formula: see text] state, our calculation is the first and predicts a bound state whose minimum is at Re = 6.8 bohr and 2.5 eV above the ground state. This state dissociates into 2P and 2S states of the Li atoms and has a hump which is higher than and outside of the hump of the B1IIu state. The long-range behavior of the states which dissociate into 2P and 2S states of the Li atom is well predicted by the resonance interaction theory.

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.

The effects of ground state correlations in 16O on the muonuclear sum rule

1982 ◽  
Vol 60 (3) ◽  
pp. 321-328 ◽  
Author(s):  
D. Duplain ◽  
B. Goulard
Keyword(s):  
Wave Function ◽  
Cluster Expansion ◽  
Ground State ◽  
Neutrino Energy ◽  
Tensor Component ◽  
Second Order ◽  
Muon Capture ◽  
Total Rate ◽  
Sum Rule ◽  
The Mean

The total rate of muon capture by 16O is calculated using the linked cluster expansion to introduce ground state correlations. All diagrams up to the second order in the number of hole-lines are included. [Formula: see text] is reduced by some 15% and is shown to behave like σ−1,. [Formula: see text] and [Formula: see text] are strongly increased by about 30%. This enhancement is related to that part of the defect wave function which arises directly from the tensor component of the N–N potential. It is suggested that, for those transitions that are induced by spin operators, the mean neutrino energy may be smaller than usually thought.

A Cluster Expansion Formalism for Direct Calculation of Ionisation Potential and Excitation Energy of Many Electron Systems Using H-F Ground State as Vacuum

1978 ◽  
Vol 33 (12) ◽  
pp. 1549-1551
Author(s):  
D. Mukherjee ◽  
A. Mukhopadhyay ◽  
R. K. Moitra
Keyword(s):  
Excitation Energy ◽  
Cluster Expansion ◽  
Ground State ◽  
Shell Theory ◽  
State Energy ◽  
Direct Calculation ◽  
Electron System ◽  
Open Shell ◽  
Electron Systems ◽  
Ionisation Potential

Abstract In this note, the authors’ recently developed non-perturbative open-shell theory is adapted for direct calculation o f ionisation potential and excitation energy of m any-electron systems. The H -F ground state is used as the “vacuum ” or “ core” in order to achieve a transparent separation o f the ground state energy. An application to a simple 4 π-electron system is discussed as an illustration o f the workability of the theory.

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

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.

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