Email this article SEARCH FOR BOUND STATES IN A ONE-DIMENSIONAL QUANTUM SYSTEM USING THE POWER METHOD: PRACTICAL IMPLEMENTATION
- Authors: Vrublevskaya N.R.1,2, Shipilo D.E.1,2, Ilyushin P.Y.1,2, Nikolaeva I.A1,2, Kosareva O.G.1,2, Panov N.A1,2
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Affiliations:
- Faculty of Physics, Lomonosov Moscow State University
- Lebedev Physical Institute of the Russian Academy of Sciences
- Issue: Vol 166, No 5 (2024)
- Pages: 612-617
- Section: ATOMS, MOLECULES, OPTICS
- URL: https://journals.rcsi.science/0044-4510/article/view/268670
- DOI: https://doi.org/10.31857/S004445102411004X
- ID: 268670
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Abstract
For numerical solution of the time-dependent Schrödinger equation describing the electron evolution in a given potential interacting with the high-intensity ultrashort pulse field, one has to find bound states of this potential with high accuracy. The paper considers the application of power algorithm using Chebyshev operator polynomials to search for bound states of one-dimensional quasi-Coulomb potential. The algorithm convergence improves with increasing polynomial degree m, saturating at m ≥ 8. For such degree, the ground state is found in ~103 Hamiltonian calculation operations, while higher states require ~105 operations (several seconds and several minutes respectively).
About the authors
N. R. Vrublevskaya
Faculty of Physics, Lomonosov Moscow State University; Lebedev Physical Institute of the Russian Academy of Sciences
Email: schipilo.daniil@physics.msu.ru
Russian Federation, 119991, Moscow; 119991, Moscow
D. E. Shipilo
Faculty of Physics, Lomonosov Moscow State University; Lebedev Physical Institute of the Russian Academy of Sciences
Email: schipilo.daniil@physics.msu.ru
Russian Federation, 119991, Moscow; 119991, Moscow
P. Ya Ilyushin
Faculty of Physics, Lomonosov Moscow State University; Lebedev Physical Institute of the Russian Academy of Sciences
Email: schipilo.daniil@physics.msu.ru
Russian Federation, 119991, Moscow; 119991, Moscow
I. A Nikolaeva
Faculty of Physics, Lomonosov Moscow State University; Lebedev Physical Institute of the Russian Academy of Sciences
Email: schipilo.daniil@physics.msu.ru
Russian Federation, 119991, Moscow; 119991, Moscow
O. G. Kosareva
Faculty of Physics, Lomonosov Moscow State University; Lebedev Physical Institute of the Russian Academy of Sciences
Email: schipilo.daniil@physics.msu.ru
Russian Federation, 119991, Moscow; 119991, Moscow
N. A Panov
Faculty of Physics, Lomonosov Moscow State University; Lebedev Physical Institute of the Russian Academy of Sciences
Author for correspondence.
Email: schipilo.daniil@physics.msu.ru
Russian Federation, 119991, Moscow; 119991, Moscow
References
- C. Eckart, Phys.Rev. 35, 1303 (1930).
- J. Javanainen, J.H. Eberly, and Q. Su, Phys. Rev.A 38, 3430 (1988).
- Е.А. Волкова, А.М. Попов, ЖЭТФ 106, 735 (1994).
- A.Popov, O.Tikhonova, and E.Volkova, J.Phys.B 32, 3331 (1999).
- M. Kolesik, J.M. Brown, A. Teleki, P. Jakobsen, J.V. Moloney, and E.M. Wright, Optica 1, 323 (2014).
- A. Bogatskaya, E. Volkova, and A. Popov, Europhys. Lett. 116, 14003 (2016).
- J. Cooley, Math.Comp. 15, 363 (1961).
- J. F. Van der Maelen Ur´ıa, S. Garc´ıa-Granda, and A. Men´endez-Vel´azquez, Amer. J.Phys. 64, 3 (1996).
- R. Kosloff and H. Tal-Ezer, Chem.Phys. Lett. 127, 223 (1986).
- M. Feit, J. Fleck, Jr., and A. Steiger, J.Comput.Phys. 47, 412 (1982).
- Р.П. Федоренко. Введение в вычислительную физику: Учебное пособие для вузов, под ред. А.И. Лобанова, Издательский дом «Интеллект», Долгопрудный (2008).
- X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, and A. Sch¨adle, Commun.Comput.Phys. 4, 729 (2008).
- X. Antoine, C. Besse, M. Ehrhardt, and P. Klein, Modeling Boundary Conditions for Solving Stationary Schr¨odinger Equations, Preprint 10/04 of the Chairs of Applied Mathematics & Numerical Analysis and Optimization and Approximation, University of Wuppertal, February (2010).
- M. Nurhuda and A. Rouf, Phys.Rev.E 96, 033302 (2017).
- Л.Д. Ландау, Е.М. Лифшиц, Квантовая механика: Нерелятивистская теория, Наука, Москва (1989).
- Н. Врублевская, Д.Шипило, И. Николаева, H. Панов, O. Косарева, Письма в ЖЭТФ 117, 400 (2023).
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