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.

Liquid 4He: Equation of State, Compressibility and Velocity of First Sound

1998 ◽  
Vol 12 (21) ◽  
pp. 2115-2127 ◽  
Author(s):  
B. Skjetne ◽  
E. Østgaard
Keyword(s):  
Wave Function ◽  
Equation Of State ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Experimental Results ◽  
Interaction Models ◽  
First Sound ◽  
Polynomial Expression ◽  
Theoretical Results

In calculations for liquid 4 He , an investigation is made to check the accuracy of a lowest-order constrained variational (LOCV) method, using modified "healing" conditions on the two-body Jastrow wave function. Results obtained for the ground-state energy for four different interaction models are fitted by a polynomial expression, whereby the pressure, compressibility and velocity of first sound are obtained. The theoretical results are found to be in fair agreement with experimental results.

EXCITON IN ZnO FILM

2007 ◽  
Vol 21 (31) ◽  
pp. 5237-5245 ◽  
Author(s):  
HUA ZHAO ◽  
WEN XIONG ◽  
MENG-ZAO ZHU
Keyword(s):  
Wave Function ◽  
Film Thickness ◽  
Effective Mass ◽  
Ground State Energy ◽  
Ground State ◽  
Quantum Tunneling ◽  
State Energy ◽  
Zno Film ◽  
Mass Approximation ◽  
Exciton Wave Function

The present study variationally calculates the ground state energy and the first excited energy of an exciton in an ZnO film in effective mass approximation. Change of the ground state energy, the first excited energy of an exciton, and radius of the exciton with film thickness are studied, as well as the correction due to the quantum tunneling of the exciton wave function through the film.

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 The Dilute Fermi Gas via Bogoliubov Theory

2021 ◽  
Author(s):  
Marco Falconi ◽  
Emanuela L. Giacomelli ◽  
Christian Hainzl ◽  
Marcello Porta
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Particle Density ◽  
Scattering Length ◽  
Three Dimensions ◽  
Positive Interaction ◽  
Interaction Potentials ◽  
Bogoliubov Theory ◽  
Regular Class

AbstractWe study the ground state properties of interacting Fermi gases in the dilute regime, in three dimensions. We compute the ground state energy of the system, for positive interaction potentials. We recover a well-known expression for the ground state energy at second order in the particle density, which depends on the interaction potential only via its scattering length. The first proof of this result has been given by Lieb, Seiringer and Solovej (Phys Rev A 71:053605, 2005). In this paper, we give a new derivation of this formula, using a different method; it is inspired by Bogoliubov theory, and it makes use of the almost-bosonic nature of the low-energy excitations of the systems. With respect to previous work, our result applies to a more regular class of interaction potentials, but it comes with improved error estimates on the ground state energy asymptotics in the density.

STUDY OF THE EXCITED STATE OF DOUBLE-Λ HYPERNUCLEI BY HYPERSPHERICAL SUPERSYMMETRIC APPROACH

2001 ◽  
Vol 10 (02) ◽  
pp. 107-127 ◽  
Author(s):  
MD. ABDUL KHAN ◽  
TAPAN KUMAR DAS ◽  
BARNALI CHAKRABARTI
Keyword(s):  
Wave Function ◽  
Excited State ◽  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy ◽  
First Excited State ◽  
Three Body ◽  
Partner Potential

Hyperspherical harmonics expansion (HHE) method has been applied to study the structure and ΛΛ dynamics for the ground and first excited states of low and medium mass double-Λ hypernuclei in the framework of core+Λ+Λ three-body model. The ΛΛ potential is chosen phenomenologically while core-Λ potential is obtained by folding the phenomenological Λ N interaction into the density distribution of the core. The parameters of this effective Λ N potential is obtained by the condition that they reproduce the experimental (or empirical) data for core-Λ subsystem. The three-body (core+Λ+Λ) Schrödinger equation is solved by hyperspherical adiabatic approximation (HAA) to get the ground state energy and wave function. This ground state energy and wave function are used to construct a partner potential. The three-body Schrödinger equation is solved once again for this partner potential. According to supersymmetric quantum mechanics, the ground state energy of this potential is exactly the same as that of the first excited state of the potential used in the first step. In addition to the two-Λ separation energy for the ground and first excited state, some geometrical quantities for the ground state of double-Λ hypernuclei [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are computed. These include the ΛΛ bond energy and various r.m.s. radii.

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