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.

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.

UNIFORM UPPER BOUNDS IN THE FRÖHLICH POLARON THEORY

1993 ◽  
Vol 07 (27) ◽  
pp. 1773-1779 ◽  
Author(s):  
N.N. BOGOLUBOV ◽  
A.V. SOLDATOV
Keyword(s):  
Interaction Parameter ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Upper Bounds ◽  
Simple Method ◽  
Polaron Theory

We present a very simple method to derive the upper bound of the ground-state energy for the Fröhlich polaron theory. The obtained bounds are proved to be uniform for all values of the interaction parameter.

VARIATIONAL APPROACH TO POLARON PROBLEM

1987 ◽  
Vol 01 (01) ◽  
pp. 89-102 ◽  
Author(s):  
N.N. BOGOLUBOV ◽  
A.N. KIREEV ◽  
A.M. KURBATOV
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Variational Approach ◽  
State Energy ◽  
Interaction Strength ◽  
Upper Bounds ◽  
Minimal Solution ◽  
Strong Interactions ◽  
Simple Models

Variational Ansatz to describe the ground state of Fröhlich’s Polaron at all interaction strength is proposed. The best upper bounds to the polaron ground state energy are obtained in the limiting cases of weak and strong interactions. For intermediate couplings two simple models are investigated. The ground state energy does not exceed their minimal solution.

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.

scholarly journals 1/ε problem in resurgence

2020 ◽  
Author(s):  
Naohisa Sueishi
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Saddle Points ◽  
Integral Formalism ◽  
Resolvent Method ◽  
Divergent Behavior ◽  
The Relationship

Abstract This paper considers the 1/ε problem, which is the divergent behavior of the ground state energy of asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and resurgence technique. Using resolvent method, It is shown that including not only one complex bion but multi-complex bion and multi-bounce contributions solves this problem. This result indicates the importance of summing all possible saddle points contribution and also the relationship between exact WKB and path integral formalism.

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
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