scholarly journals A lower bound for the BCS functional with boundary conditions at infinity

2017 ◽  
Vol 58 (8) ◽  
pp. 081901 ◽  
Author(s):  
Andreas Deuchert
Keyword(s):  
Lower Bound ◽  
Boundary Conditions ◽  
Conditions At Infinity

Semibounded Extensions of Singular Ordinary Differential Operators

1988 ◽  
Vol 31 (4) ◽  
pp. 432-438
Author(s):  
Allan M. Krall
Keyword(s):  
Differential Operator ◽  
Lower Bound ◽  
Boundary Conditions ◽  
Differential Operators ◽  
The Self ◽  
Limit Circle ◽  
Singular Differential Operator ◽  
Ordinary Differential Operators

AbstractThe self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.

Proper Boundary Conditions for Infinitely Layered Orthotropic Media

2000 ◽  
Vol 67 (3) ◽  
pp. 629-632
Author(s):  
E. L. Bonnaud ◽  
J. M. Neumeister
Keyword(s):  
Boundary Conditions ◽  
Layered Medium ◽  
Integral Transforms ◽  
Numerical Treatment ◽  
Problem Size ◽  
Transfer Matrix Approach ◽  
Stress Functions ◽  
Orthotropic Media ◽  
First Time ◽  
Conditions At Infinity

A stress analysis of a plane infinitely layered medium subjected to surface loadings is performed using Airy stress functions, integral transforms, and a revised transfer matrix approach. Proper boundary conditions at infinity are for the first time established, which reduces the problem size by one half. Methods and approximations are also presented to enable numerical treatment and to overcome difficulties inherent to such formulations. [S0021-8936(00)01103-X]

Boundary Conditions at Infinity for a Single Blocking Electrode

1964 ◽  
Vol 41 (5) ◽  
pp. 1505-1506 ◽  
Author(s):  
Ian R. Gatland ◽  
Louis Gold ◽  
John W. Moffat
Keyword(s):  
Boundary Conditions ◽  
Conditions At Infinity

On the theory of elastic collisions between electrons and hydrogen atoms

1960 ◽  
Vol 254 (1277) ◽  
pp. 259-272 ◽  
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Boundary Conditions ◽  
Continuous Spectrum ◽  
Ground State ◽  
Wave Functions ◽  
Hydrogen Atoms ◽  
Complete Set ◽  
Exchange Scattering ◽  
Conditions At Infinity

A hydrogen atom in the ground state scatters an electron with kinetic energy too small for inelastic collisions to occur. The wave function Ψ(r 1 ; r 2 ) of the system has boundary conditions at infinity which must be chosen to allow correctly for the possibilities of both direct and exchange scattering. The expansion Ψ = Σ ψ,(r 1 )F y (r 2 ) of the total wave function in y terms of a complete set of hydrogen atom wave functions ψ y (r 1 ) includes an integration over the continuous spectrum. It is si own that the integrand contains a singularity. The explicit form of this singularity and its connexion with the boundary conditions are examined in detail. The symmetrized functions Y* may be represented by expansions of the form Σ {ψ y (r 1 ) G y ±(r 2 ) ±ψ y (r 2 ) y G y ±(r 1 )}, where the integrand in the continuous spectrum does not involve singularities. Finally, it is shown that because all the states ψ y of the hydrogen atom are included in the expansion, the equation satisfied by F 1 , the coefficient of the ground state, contains a polarization potential which behaves like — a/2 r 4 for large r and is independent of the velocity of the incident electron.

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