Variational method for the free-energy approximation of generalized anharmonic oscillators

1993 ◽  
Vol 47 (2) ◽  
pp. 838-846 ◽  
Author(s):  
K. Vlachos
Keyword(s):  
Free Energy ◽  
Variational Method ◽  
Anharmonic Oscillators ◽  
Energy Approximation

An improved way of minimizing free energy in the variational method with the square well reference system

2017 ◽  
Vol 62 (5) ◽  
pp. 240-243 ◽  
Author(s):  
N. E. Dubinin ◽  
V. V. Filippov ◽  
A. A. Yuryev ◽  
N. A. Vatolin
Keyword(s):  
Free Energy ◽  
Variational Method ◽  
Reference System ◽  
Square Well

Effects of free energy approximation on superconducting surface sheath calculations

1967 ◽  
Vol 24 (13) ◽  
pp. 711-712
Author(s):  
W.R. Bandy ◽  
C.R. Haden ◽  
T.D. Shockley
Keyword(s):  
Free Energy ◽  
Energy Approximation

Dirichlet and von Neumann Basis Set for Quantum Mechanical Anharmonic Oscillators

1983 ◽  
Vol 38 (4) ◽  
pp. 473-476 ◽  
Author(s):  
Alejandro M. Mesón ◽  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Variational Method ◽  
Harmonic Oscillator ◽  
Lower Bounds ◽  
Neumann Boundary ◽  
Basis Set ◽  
Basis Sets ◽  
Upper And Lower Bounds ◽  
Quantum Mechanical ◽  
Anharmonic Oscillators ◽  
Von Neumann

It is shown that accurate upper and lower bounds to the eigenvalues of anharmonic oscillators can be obtained by means of the Rayleigh-Ritz variational method and two trigonometric basis sets of functions which satisfy Dirichlet and Von Neumann boundary conditions. Numerical results show that the Dirichlet basis set is more appropriate than the harmonic oscillator one for calculating eigenvalues and the value of eigenfunctions at the origin.

scholarly journals LOWEST ORDER CONSTRAINED VARIATIONAL CALCULATION FOR POLARIZED LIQUID 3He AT FINITE TEMPERATURE

2009 ◽  
Vol 23 (01) ◽  
pp. 113-123 ◽  
Author(s):  
G. H. BORDBAR ◽  
M. J. KARIMI ◽  
J. VAHEDI
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Variational Method ◽  
Specific Heat ◽  
Finite Temperature ◽  
Variational Calculation ◽  
Saturation Density ◽  
Energy Entropy ◽  
Spin Polarized

We have investigated some of the thermodynamic properties of spin-polarized liquid 3 He at finite temperature using the lowest order constrained variational method. For this system, the free energy, entropy and pressure are calculated for different values of the density, temperature and polarization. We have also presented the dependence of specific heat, saturation density and incompressibility on temperature and polarization.

scholarly journals Temperature dependence of the Helmholtz free energy of liquid alkali metals

BIBECHANA ◽  
2012 ◽  
Vol 9 ◽  
pp. 7-12
Author(s):  
BK Singh ◽  
Sudhir Singh
Keyword(s):  
Free Energy ◽  
Correlation Function ◽  
Variational Method ◽  
Temperature Dependence ◽  
Alkali Metals ◽  
Helmholtz Free Energy ◽  
Model Potential ◽  
Type Model ◽  
Liquid Alkali Metals ◽  
Good Agreement

The Gibbs-Bogoliubov variational method has been considered to study the Helmholtz free energy of liquid alkali metals (Na, K, Rb and Cs) as a function of temperature, using Heine Abarenkov type model potential with Hubbard-Sham exchange and correlation function. The computed values are in very good agreement with experimental observations. DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7144 BIBECHANA 9 (2013) 7-12

Lower bound approximation to the free energy of an Ising model on a simple cubic lattice

1981 ◽  
Vol 59 (10) ◽  
pp. 1291-1295 ◽  
Author(s):  
Chin-Kun Hu ◽  
Wen-Den Chen ◽  
Yu-Ming Shih ◽  
Dong-Chung Jou ◽  
C. K. Pan ◽  
...  
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Lower Bound ◽  
Variational Method ◽  
Critical Point ◽  
Zero Field ◽  
Free Energies ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We apply a modified Kadanoff's variational method to calculate the lower bound zero-field free energies and their derivatives for an Ising model on the simple cubic lattice. We find a critical point at Kc = 0.2393769 with precision ±10−7.

scholarly journals Zur Theorie des nichtlokalen Supraleiters im Magnetfeld

1968 ◽  
Vol 23 (11) ◽  
pp. 1822-1833
Author(s):  
W. Schattke
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Variational Method ◽  
Order Parameter ◽  
Diffuse Reflection ◽  
Bcs Theory ◽  
Pair Breaking ◽  
Perturbation Calculation ◽  
Variational Equations ◽  
Non Local

Starting from the BCS-Theory, an upper bound for the free energy is obtained by a combination of a variational method and perturbation theory. The variational equations obtained are non-local. The parameters of the perturbation calculation are the vector potential and the spatial variations of the order parameter, which have to be small. Boundary conditions are set for the case of diffuse reflection and pair-breaking at the surface. As an example, the superconducting plate is discussed.

scholarly journals New Variational Method for the Free Energy

1984 ◽  
Vol 71 (6) ◽  
pp. 1413-1415 ◽  
Author(s):  
A. Oguchi
Keyword(s):  
Free Energy ◽  
Variational Method
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