Approximation of the time-dependent electronic Schrödinger equation by MCTDHF

Applied Mathematics and Computation

Volumn 173, Issue 2, 2006, Pages 960-976

  Koch, Othmar ^a,b   Kreuzer, Wolfgang ^a   Scrinzi, Armin ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Dirac Frenkel principle; Method of lines; Multi configuration time dependent Hartree Fock method; Pseudospectral method; Runge Kutta methods; Splitting methods; Time dependent Schr dinger equation; Ultrafast laser dynamics; Variational approximation

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; NUMERICAL METHODS; RUNGE KUTTA METHODS;

DIRAC-FRENKEL PRINCIPLE; METHOD OF LINES; PSEUDOSPECTRAL METHODS; SPLITTING METHODS; ULTRAFAST LASER DYNAMICS; VARIATIONAL APPROXIMATION;

NONLINEAR EQUATIONS;

EID: 32644439415     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.04.027     Document Type: Article

References (26)

1. J. Zanghellini, M. Kitzler, C. Fabian, T. Brabec, and A. Scrinzi An MCTDHF approach to multi-electron dynamics in laser fields Laser Phys. 13 8 2003 1064 1068
2. J. Zanghellini, M. Kitzler, T. Brabec, and A. Scrinzi Testing the multi-configuration time-dependent Hartree-Fock method J. Phys. B: At. Mol. Phys. 37 2004 763 773
3. F. Krausz, and T. Brabec Intense few-cycle laser fields: frontiers of nonlinear optics Rev. Mod. Phys. 72 2000 545 562
4. R. Kienberger, M. Hentschel, M. Uiberacker, C. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz Steering attosecond electron wave packets with light Science 297 2002 1144 1148
5. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz Time-resolved atomic inner-shell spectroscopy Nature 419 2002 803 807
6. A. Bandrauk, and A. Chelkowski On laser Coulomb explosion imaging of proton motion Chem. Phys. Lett. 336 2001 518 522
7. J.S. Parker, L. Moore, and K. Taylor Accurate computational methods for two-electron atom-laser interactions Optics-Express 8 2001 436 441
8. V. Veniard, R. Taieb, and A. Maquet Photoionization of atoms using time-dependent density functional theory Laser Phys. 13 2003 465 474
9. J. Caillat, J. Zanghellini, M. Kitzler, W. Kreuzer, O. Koch, and A. Scrinzi Correlated multielectron systems in strong laser pulses-an MCTDHF approach Phys. Rev. A 71 2005 012712
10. L.D. Landau, and E.M. Lifshitz Quantum Mechanics: Non-Relativistic Theory third ed. 1977 Pergamon Press Oxford-New York
11. M.H. Beck, A. Jäckle, G.A. Worth, and H.-D. Meyer The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets Phys. Rep. 324 2000 1 105
12. M.H. Beck, and H.-D. Meyer An efficient and robust integration scheme for the equations of the multiconfiguration time-dependent Hartree (MCTDH) method Z. Phys. D 42 1997 113 129
13. C. Lubich A variational splitting integrator for quantum molecular dynamics Appl. Numer. Math. 48 2004 355 368
14. P. Dirac Note on exchange phenomena in the Thomas atom Proc. Cambridge Phil. Soc. 26 1939 376 385
15. J. Frenkel Wave Mechanics, Advanced General Theory 1934 Clarendon Press Oxford
16. C. Lubich On variational approximations in quantum molecular dynamics Math. Comp. 74 2005 765 779
17. O. Koch, W. Kreuzer, A. Scrinzi, MCTDHF in ultrafast laser dynamics, AURORA TR-2003-29, Inst. for Appl. Math. and Numer. Anal., Vienna Univ. of Technology, Austria, 2003. Available from: .
18. H.W. Alt Lineare Funktionalanalysis third ed. 1999 Springer-Verlag Berlin-Heidelberg-New York
19. A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations 1983 Springer-Verlag New York
20. T. Klett, Regularität und Approximation im Multikonfigurations- Hartree-Verfahren der Quantendynamik, Master Thesis, Eberhard Karls Universität Tübingen, 2004.
21. L. Trefethen Spectral Methods in MATLAB 2000 SIAM Philadelphia
22. T. Jahnke, and C. Lubich Error bounds for exponential operator splittings BIT 40 2000 735 744
23. R. Kosloff Quantum molecular dynamics on grids R.E. Wyatt J.Z. Zhang Dynamics of Molecules and Chemical Reactions 1996 Marcel Dekker New York 185 230
24. O. Koch, W. Kreuzer, Performance of MCTDHF implementations, AURORA TR-2004-14, Inst. for Anal. and Sci. Comput., Vienna Univ. of Technology, Austria, 2004. Available from: .
25. O. Koch Numerical solution of the time-dependent Schrödinger equation in ultrafast laser dynamics WSEAS Trans. Math. 3 2004 584 590
26. E. Hairer, C. Lubich, and G. Wanner Geometric Numerical Integration 2002 Springer-Verlag Berlin-Heidelberg-New York