UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2026-06-11 23:58
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Conference: Bucharest University Faculty of Physics 2026 Meeting


Section: Theoretical and Computational Physics, Applied Mathematics


Title:
Green's function reconstruction using B-Splines in finite potential wells


Authors:
Andrei Vlad IANAC (1), Cristian IORGA (1,2)


Affiliation:
1) Faculty of Physics, University of Bucharest, Strada Atomistilor 405, 077125 Bucharest, Romania

2)National Institute for Laser, Plasma and Radiation Physics, Strada Atomistilor 409, 077125 Magurele, Romania


E-mail
vladianac4@gmail.com


Keywords:
B-Splines, Non-orthogonal polynomials, Green's function, two-photon decay, finite potential well


Abstract:
We employed the B-Spline approach in constructing Green's function in asymmetrical finite potential wells for treating the higher-order perturbation processes, such as two-photon decay or photon scattering. First, we obtained the finite potential well's bound states using semi-analytical procedures, after which we fine-tuned the parameters of the B-Splines: spatial domain, number of splines, and spline order, in order to reproduce the discrete states with increasing accuracy. This method also provided a dense resolution of pseudo-levels representing the continuum energy states. Next, we verified the Thomas-Reiche-Kuhn sum rules in length and velocity gauges using both the semi-analytical results and the B-Splines' states. It is of note that the completeness relation using B-Splines is assured even for lower spline orders and fewer polynomials, while using explicit bound and continuum energy states to reach the same results is significantly more computationally-taxing. We computed the two-photon decay rate of the first excited state of the asymmetrical finite potential wells, using second-order perturbation theory and summation over all available intermediate states. For this purpose, Green's function has been contructed using the pseudo-spectral method both via B-Splines and using explicit discrete and continuum energy eigenstates.


References:

1. N. Zettili, Quantum Mechanics: Concepts and Applications, 2nd ed., Wiley, 2009.

2. C. de Boor, A Practical Guide to Splines, revised ed., Springer, 2001.

3. W. R. Johnson, S. A. Blundell, and J. Sapirstein,

“Finite basis sets for the Dirac equation constructed from B splines,”

Physical Review A, vol. 37, no. 2, pp. 307–315, 1988.

4. H. Bachau, E. Cormier, P. Decleva, J. E. Hansen, and F. Martín,

“Applications of B-splines in atomic and molecular physics,”

Reports on Progress in Physics, vol. 64, no. 12, pp. 1815–1943, 2001.