Reduced Green's Function for the Ground State of the Hydrogen Atom

1969 ◽  
Vol 184 (1) ◽  
pp. 245-246 ◽  
Author(s):  
Ronald J. White
Keyword(s):  
Hydrogen Atom ◽  
Green’S Function ◽  
Green's Function ◽  
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.

Temperature Effect on Cirac and Zoller Model Using Two-Time Green's Function

2003 ◽  
Vol 17 (13n14) ◽  
pp. 743-753
Author(s):  
Wei Li ◽  
Hong-Min Zhao ◽  
Jia-Tih Lin
Keyword(s):  
Green’S Function ◽  
Temperature Effect ◽  
Quantum Computation ◽  
Green's Function ◽  
Ground State ◽  
Function Method ◽  
State Energy ◽  
Internal State ◽  
Trap Frequency ◽  
Upper Limit

Using the two-time Green's function method, we analyze the temperature effect on the famous Cirac and Zoller model. Formulas for the average number of different mode phonons and the deviation of its internal state from its ground state are derived. The influence of the internal state energy and trap frequency on the number of phonons is also discussed. The upper limit of temperature for regular quantum computation in the Cirac and Zoller model is obtained.

Precise theory of the Stark effect on hydrogen- and helium-like atoms

2002 ◽  
Vol 80 (11) ◽  
pp. 1401-1412 ◽  
Author(s):  
V D Ovsiannikov ◽  
V G Pal'chikov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ground State ◽  
Stark Effect ◽  
Energy Levels ◽  
Relativistic Effects ◽  
Model Potential ◽  
Matrix Elements ◽  
Angular Momenta ◽  
Relativistic Coulomb

The relativistic effects on the dipole polarizabilities and hyperpolarizabilities are considered for different kinds of energy levels in hydrogen- and helium-like atoms. The relativistic Coulomb Green's function is used for calculating the susceptibilities of the ground-state hydrogen up to terms of order (α Z)10. Both relativistic and interelectronic corrections are determined for the ground state of helium. The formulas are given for polarizability and hyperpolarizability in the relativistic "screened-charge" approximation. The anticrossing of the triplet 3PJ states with zero magnetic quantum number is studied on the basis of perturbation theory for degenerate states. General expressions are given for the dipole matrix elements, up to the fourth order in field strength, within the basis of close fine-structure substates with equal angular momenta L and different total momenta J. The calculation of the higher order matrix elements is carried out with the use of the Green's function in the model potential approximation. PACS Nos.: 31.10Dk, 31.15Ar, 31.30Jv, 32.10-f, 31.25Eb

scholarly journals Self-interaction in Green’s-function theory of the hydrogen atom

2007 ◽  
Vol 75 (3) ◽  
Author(s):  
W. Nelson ◽  
P. Bokes ◽  
Patrick Rinke ◽  
R. W. Godby
Keyword(s):  
Hydrogen Atom ◽  
Green’S Function ◽  
Green's Function ◽  
Function Theory
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