Determination of core polarizabilities in sodium by numerical integration of Schrödinger’s equation

1985 ◽  
Vol 32 (5) ◽  
pp. 2569-2572 ◽  
Author(s):  
James C. Lombardi
Keyword(s):  
Numerical Integration ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

Numerically Efficient Computation of Eigensolution Spectrum in One-Dimensional Heterostructures

1998 ◽  
Vol 09 (07) ◽  
pp. 927-934 ◽  
Author(s):  
F. Farrelly ◽  
A. Petri
Keyword(s):  
Transfer Matrix ◽  
Density Of States ◽  
Spatial Behavior ◽  
Efficient Computation ◽  
Matrix Methods ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

We describe a method that allows an efficient determination of the density of states of one-dimensional heterostructures. We show that the propagation of an appropriate vector through the structure together with the use of the node theorem is much more effective than transfer matrix methods in those cases in which highly degenerate spectra are present. As a by-product, spatial behavior of solutions is also easily obtained. A case of elastic propagation is discussed in detail and application to Schrödinger's equation is presented.

scholarly journals Orthogonal structure on a quadratic curve

2020 ◽  
Author(s):  
Sheehan Olver ◽  
Yuan Xu
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Extension Problem ◽  
Orthogonal Expansions ◽  
Schrödinger’S Equation ◽  
Fourier Extension ◽  
Quadratic Curve ◽  
Interpolation Of Functions ◽  
Fourier Orthogonal Expansions ◽  
Schrödinger's Equation

Abstract Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger’s equation with nondifferentiable or nearly nondifferentiable potentials.

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