Quasi Sturmian Functions in Problems of a Three-Particle Coulomb Continuum

2015 ◽  
Vol 58 (7) ◽  
pp. 941-951 ◽  
Author(s):  
M. S. Aleshin ◽  
S. A. Zaitsev ◽  
G. Gasaneo ◽  
L. U. Ancarani
Keyword(s):  
Sturmian Functions

Analytic Sturmian functions and convergence of separable expansions

1987 ◽  
Vol 36 (2) ◽  
pp. 475-484 ◽  
Author(s):  
K. Hartt ◽  
P. V. A. Yidana
Keyword(s):  
Sturmian Functions

scholarly journals Using ‘dressed’ convoluted quasi-Sturmian functions as a basis for Coulomb three-body continuum problems

2020 ◽  
Vol 1412 ◽  
pp. 152028
Author(s):  
A S Zaytsev ◽  
D S Zaytseva ◽  
L U Ancarani ◽  
S A Zaytsev
Keyword(s):  
Three Body ◽  
Sturmian Functions

scholarly journals The quantum-mechanical Coulomb propagator in an L2 function representation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rolf Gersbacher ◽  
John T. Broad
Keyword(s):  
Recursion Relation ◽  
Contour Integral ◽  
Quantum Mechanical ◽  
Stieltjes Integral ◽  
Pollaczek Polynomials ◽  
Discrete Part ◽  
Legendre Quadrature ◽  
The Continuum ◽  
Square Integrable Basis ◽  
Sturmian Functions

AbstractThe quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated. The Coulomb propagator generally consists of two parts. The sum of the discrete part of the spectrum is extrapolated numerically, while three integration procedures are applied to the continuum part of the oscillating integral: the Gauss–Pollaczek quadrature, the Gauss–Legendre quadrature along the real axis, and a transformation into a contour integral in the complex plane with the subsequent Gauss–Legendre quadrature. Using the contour integral, the Coulomb propagator can be calculated very accurately from an L$$^2$$ 2 basis. Using the three-term recursion relation of the Pollaczek polynomials, an effective algorithm is herein presented to reduce the number of integrations. Numerical results are presented and discussed for all procedures.

Sturmian Functions

2018 ◽  
pp. 153-176
Author(s):  
George Rawitscher ◽  
Victo dos Santos Filho ◽  
Thiago Carvalho Peixoto
Keyword(s):  
Sturmian Functions
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