Abstract
The operator-difference multi-layer (ODML) schemes for solving the time-dependent Schrödinger equation (TDSE) till six order accuracy by a time step are presented. The reduced schemes for solving a set of the coupled TDSE’s are devised by using a set of appropriate basis angular functions and a finite element method with respect to a hyper-radial variable. Convergence by a number of the basis functions and efficiency of the numerical schemes are demonstrated in the case of an exactly solvable model of the two-dimensional oscillator in time-depended electric fields.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. G. Butkovskiy and Yu. I. Samoilenko, Control of Quantum-Mechanical Processes and Systems (Kluwer Academic Publishers, Dordrecht Hardbound, 1990).
S. Misicu, M. Rizea, and W. Greiner, J. Phys. G 27, 993–1003 (2001).
V. V. Serov et al., Proc. SPIE Int. Soc. Opt. Eng. 6537, 65370Q-1–7 (2007).
I. V. Puzynin et al., PEPAN. 38, 144–232 (2007) [Phys. Part. Nucl. Lett. 38, 70–116 (2007)].
O. Chuluunbaatar et al., Comput. Phys. Commun. 177, 649–675 (2007).
V. V. Pupyshev, Fiz. Elem. Chast. i Atom. Yad. 35, 256–347 (2004), [Phys. Part. Nucl. 35, 145–192 (2004)].
O. Chuluunbaatar et al., Comput. Phys. Commun. (2007), doi:10.1016/j.cpc.2007.09.005.
V. S. Melezhik, J. I. Kim, and P. Schmelcher, Phys. Rev. A 76, 053611-1–15 (2007).
A. Gusev et al., Pis’ma v ECHAYA 38, 253–259 (2007) [Phys. Part. Nucl. Lett. 38, 146–149 (2007)].
K. J. Bathe, Finite Element Procedures in Engineering Analysis (Prentice Hall, New York, Englewood Cliffs, NJ, 1982).
A. G. Abrashkevich, M. S. Kaschiev, and S. I. Vinitsky, J. Comp. Phys. 163, 328–348 (2000).
H. A. Sarkisyan, Mod. Phys. Lett. B 16, 835–841 (2002).
Yu. N. Demkov and J. D. Meyer, Eur. Phys. J. B 42, 361–365 (2004).
Sh. A. Kalandarov et al., Phys. Rev. E 75, 031115-1–16 (2007).
Author information
Authors and Affiliations
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Chuluunbaatar, O., Gerdt, V.P., Gusev, A.A. et al. Multi-layer evolution schemes for the finite-dimensional quantum systems in external fields. Phys. Part. Nuclei Lett. 6, 550–553 (2009). https://doi.org/10.1134/S1547477109070127
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477109070127