The upper and lower bounds of the ground state energies using the variational method

1987 ◽  
Vol 55 (11) ◽  
pp. 1039-1040 ◽  
Author(s):  
Johnson Lee
Keyword(s):  
Variational Method ◽  
Lower Bounds ◽  
Ground State ◽  
Upper And Lower Bounds ◽  
Ground State Energies

Converging upper and lower bounds for ground-state energies of atomic nuclei

2005 ◽  
Vol 25 (3) ◽  
pp. 379-385
Author(s):  
G. P. Kamuntavičius ◽  
D. Germanas ◽  
R. K. Kalinauskas ◽  
S. Mickevičius ◽  
R. Žemaičinienė
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
Upper And Lower Bounds ◽  
Atomic Nuclei ◽  
Ground State Energies

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.

Lower bounds for the ground-state energies of the two-dimensional Hubbard andt-Jmodels

1991 ◽  
Vol 43 (16) ◽  
pp. 13743-13746 ◽  
Author(s):  
Roser Valent ◽  
Joachim Stolze ◽  
P. J. Hirschfeld
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
Two Dimensional ◽  
Ground State Energies

Lower-bound energies and the Virial theorem in wave mechanics

1961 ◽  
Vol 57 (2) ◽  
pp. 341-347 ◽  
Author(s):  
G. L. Caldow ◽  
C. A. Coulson
Keyword(s):  
Wave Function ◽  
Lower Bound ◽  
Variational Method ◽  
Harmonic Oscillator ◽  
Lower Bounds ◽  
Ground State ◽  
Virial Theorem ◽  
Wave Functions ◽  
Wave Mechanics ◽  
Mechanical Problem

ABSTRACTSeveral forms of the lower-bound variational method for the calculation of the eigenvalues in a wave-mechanical problem are considered, and compared; the particular case of the harmonic oscillator being chosen. All forms have certain unsatisfactory features, but some of them are considerably worse than others. One reason why calculations of lower bounds are in general less satisfactory than Ritz-type calculations of an upper bound is shown to be that whereas, in the presence of a scale factor, this latter wave-function satisfies the virial theorem, in none of the lower-bound wave-functions is this true. Similar calculations are reported for the ground state of the helium atom.

A procedure for obtaining lower bounds for ground state energies of atoms and molecules

1969 ◽  
Vol 13 (2) ◽  
pp. 155-158
Author(s):  
M. Bersohn ◽  
M. Glicksohn ◽  
J. Stewart
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
Atoms And Molecules ◽  
Ground State Energies

scholarly journals Upper and lower bounds for tunneling splittings in a symmetric double-well potential

RSC Advances ◽  
2020 ◽  
Vol 10 (57) ◽  
pp. 34681-34689
Author(s):  
Miklos Ronto ◽  
Eli Pollak
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ground State ◽  
Upper And Lower Bounds ◽  
Tunneling Splittings ◽  
Double Well Potential

Ground state tunneling gaps: solid circles are mean of eigenvalues and lower bound gaps.

Sign in / Sign up

Export Citation Format

Share Document