Variational estimate of a breakup amplitude

1983 ◽  
Vol 28 (5) ◽  
pp. 1918-1924 ◽  
Author(s):  
B. G. Giraud ◽  
M. A. Nagarajan
Keyword(s):  
Variational Estimate ◽  
Breakup Amplitude

Variational Estimate of the Energy Spectrum of a Bound Polaron

1973 ◽  
Vol 56 (1) ◽  
pp. 211-221 ◽  
Author(s):  
T. D. Clark ◽  
K. K. Bajaj
Keyword(s):  
Energy Spectrum ◽  
Variational Estimate ◽  
Bound Polaron

Coulomb difference between p+d and n+d breakup amplitude very near the threshold

1984 ◽  
Vol 144 (1-2) ◽  
pp. 19-22 ◽  
Author(s):  
H. Kröger ◽  
R.J. Slobodrian
Keyword(s):  
Breakup Amplitude

scholarly journals Variational Theory of Reflection

1985 ◽  
Vol 38 (2) ◽  
pp. 113 ◽  
Author(s):  
John Lekner
Keyword(s):  
Transverse Electric ◽  
Grazing Incidence ◽  
Interface Thickness ◽  
Variational Theory ◽  
Variational Estimate ◽  
First Order ◽  
Reflection Amplitude ◽  
Scattering Phase ◽  
Finite Barrier ◽  
Transverse Electric Wave

Schwinger's variational method for the scattering phase shift produced by a central potential is adapted to reflection by a planar potential barrier (or well). The formulation is general, for an arbitrary transition between any two media, but the application here is limited to reflection at a barrier between media of equal potential energy. The simplest variational estimate for the reflection amplitude correctly tends to -1 at grazing incidence, as it must for any finite barrier. This is in contrast to the first order perturbation reflection amplitude, which diverges at grazing incidence. The same variational estimate is also correct to second order in the ratio of the interface thickness to the wavelength of the incident wave. The theory applies also to the reflection of the electromagnetic s (or transverse electric) wave at an interface between two media.

Ground-state analysis of the Falicov-Kimball model on complete graphs

2000 ◽  
Vol 78 (7) ◽  
pp. 679-699
Author(s):  
O Bolina ◽  
D HU Marchetti
Keyword(s):  
Ground State ◽  
State Energy ◽  
Energy Gap ◽  
Complete Graphs ◽  
Variational Estimate ◽  
Finite Graphs ◽  
Exact Ground State ◽  
State Nature ◽  
Number Of Particles ◽  
Complete Account

The ground-state nature of the Falicov–Kimball model of mobile electrons and fixed nuclei on complete graphs is investigated. We give a pedagogic derivation of the eigenvalue problem and present a complete account of the ground-state energy both as a function of the number of electrons and nuclei and as a function of the total number of particles for any value of interaction U [Formula: see text] [Formula: see text]. We also study the energy gap and show the existence of a phase transition characterized by the absence of gap at the half-filled band for U < 0. The model in consideration was proposed and partially solved by Farkasovsky for finite graphs and repulsive on-site interaction U > 0. Contrary to his proposal, we conveniently scale the hopping matrix to guarantee the existence of the thermodynamic limit. We also solve this model on bipartite complete graphs and examine how sharp the Kennedy–Lieb variational estimate is as compared with the exact ground state. PACS Nos.: 71.2-b, 02.10Gd

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