Improved Lower Bounds to the Overlap Integral of an Approximate Wavefunction with the True Wavefunction

1967 ◽  
Vol 46 (6) ◽  
pp. 2448-2449 ◽  
Author(s):  
Frank Weinhold
Keyword(s):  
Lower Bounds ◽  
Overlap Integral

Stark Ladders in Crystals: Inclusion of Overlap

1974 ◽  
Vol 52 (23) ◽  
pp. 2395-2401 ◽  
Author(s):  
M. J. Richardson ◽  
S. G. Davison
Keyword(s):  
Energy Spectrum ◽  
Difference Equation ◽  
Molecular Orbital ◽  
Lower Bounds ◽  
Continued Fraction ◽  
Energy Shift ◽  
Upper And Lower Bounds ◽  
Field Perturbation ◽  
Overlap Integral ◽  
Finite Linear

The molecular orbital technique is used to study the Stark ladder effect in crystals. It is found that the field perturbation of the exchange integrals can be expressed in terms of the overlap integral. The inclusion of overlap in this way results in the Schrödinger equation being written as a hypergeometric difference equation, which is solved for both infinite and finite linear crystals. These solutions show that the overlap contribution causes an energy shift in the position of the Stark ladder, but leaves its gradient unchanged. Continued fraction properties are used to obtain the finite crystal solutions, which are expressed as upper and lower bounds of the perturbed energy spectrum.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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