Bounds on the ground state energy: Application of the variational principle

2009 ◽  
Vol 77 (1) ◽  
pp. 44-47 ◽  
Author(s):  
Bibhas Bhattacharyya
Keyword(s):  
Variational Principle ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Energy Application

GENERALIZED VARIATIONAL PRINCIPLE IN QUANTUM MECHANICS

1995 ◽  
Vol 09 (22) ◽  
pp. 2899-2936 ◽  
Author(s):  
A.V. SOLDATOV
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Quantum System ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Convergent Sequence ◽  
Upper Bounds ◽  
Generalized Variational Principle ◽  
Quantitative Characteristics

An algorithm is proposed that allows us to derive the convergent sequence of upper bounds for the ground state energy of a quantum system. The algorithm generalizes the well-known variational principle of quantum mechanics and moreover provides qualitative, and under some additional conditions even quantitative, characteristics of the spectrum of a quantum system as a whole.

scholarly journals Variational Principle Techniques and the Propertiesof a Cut-off and Anharmonic Wave Function

2009 ◽  
Vol 6 (1) ◽  
pp. 113-119 ◽  
Author(s):  
A. N. Ikot ◽  
L. E. Akpabio ◽  
K. Essien ◽  
E. E. Ituen ◽  
I. B. Obot
Keyword(s):  
Dynamical System ◽  
Wave Function ◽  
Variational Principle ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Variational Principles ◽  
Analytical Tool ◽  
Three Dimensions ◽  
Anharmonic Oscillators

The variational principles are very useful analytical tool for the study of the ground state energy of any dynamical system. In this work, we have evaluated the method and techniques of variational principle to derive the ground state energy for the harmonic, cut-off and anharmonic oscillators with a ground state wave function for a one-body Hamiltonian in three dimensions.

On the Uniform Upper Bounds to the Ground State Energy of Quantum System

1997 ◽  
Vol 11 (10) ◽  
pp. 1235-1244
Author(s):  
A. N. Kireev
Keyword(s):  
Variational Principle ◽  
Harmonic Oscillator ◽  
Quantum System ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Natural Generalization ◽  
Upper Bounds ◽  
General Character ◽  
Exact Ground State

We derive a set of improving uniform upper bounds to the ground state energy of a quantum system, which provides a natural generalization of the Ritz variational principle. The bounds have a general character, do not depend on the structure of Hamiltonian of a quantum system and converge to its exact ground state energy. As an illustration of the method proposed, we consider a simple example of the shifted harmonic oscillator.

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.

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