Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 72, Issue 1, 2005, Pages

  Gilary, Ido ^a   Fleischer, Avner ^a   Moiseyev, Nimrod ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL REFLECTIONS; PROPAGATION CALCULATIONS; WAVE PACKETS (WP);

HAMILTONIANS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

QUANTUM THEORY;

EID: 27144494542     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.72.012117     Document Type: Article

References (41)

1. B. R. Junker, Adv. At. Mol. Phys. AAMOA2 0065-2199 18, 107 (1982).
2. W. P. Reinhardt, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev.pc.33.100182.001255 33, 223 (1982).
3. Y. K. Ho, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(83)90112-6 99, 1 (1983).
4. N. Moiseyev, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98)00002-7 302, 211 (1998).
5. J. G. Muga, J. P. Palao, B. Navarro, and I. L. Equsquiza, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2004.03.002 395, 357 (2004).
6. R. Santra and L. S. Cederbaum, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00143-6 368, 1 (2002).
7. A. M. Perelomov and Ia. B. Ze\'c4\'badovich, Quantum Mechanics: Selected Topics (World Scientific, Singapore, 1998).
8. The Letropet Symposium View on Generalized Inner Product, edited by, E. BrEndas, and, N. Elander, Lecture Notes in Physics Vol. 325 (Springer, Berlin, 1989).
9. N. Moiseyev, P. R. Certain, and F. Weinhold, Mol. Phys. MOPHAM 0026-8976 36, 1617 (1978).
10. N. Moiseyev and F. Weinhold, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.2100 78, 2100 (1997).
11. R. Kosloff and D. Kosloff, J. Comput. Phys. JCTPAH 0021-9991 10.1016/0021-9991(86)90199-3 63, 363 (1986);
12. G. Ashkenazi, R. Kosloff, S. Ruhman, and H. Tal-Ezer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.469904 103, 10005 (1995).
13. C. Leforestier and R. E. Wyatt, Chem. Phys. Lett. CHPLBC 0009-2614 10.1063/1.445033 78, 2334 (1983).
14. A. Vibok and G. G. Balint-Kurti, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.462414 96, 7615 (1992);
15. G. G. Balint-Kurti, in Reaction and Molecular Dynamics, edited by, A. Laganna, and, A. Riganelli, Lecture Notes in Chemistry Vol. 75 (Springer, Berlin, 2000), p. 74.
16. E. Pahl, H. D. Meyer, L. S. Cederbaum, and F. Tarantelli, J. Electron Spectrosc. Relat. Phenom. JESRAW 0368-2048 10.1016/S0368-2048(98)00154-6 93, 17 (1998).
17. S. Scheit, L. S. Cederbaum, and H. D. Meyer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1531996 118, 2092 (2003);
18. N. Moiseyev, S. Scheit, and L. S. Cederbaum, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1709867 121, 722 (2004).
19. A. Bohm, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.861 60, 861 (1999);
20. A. Bohm and N. L. Harshman, Irreversibility and Causality, edited by, A. Bohm, H.-D. Doebner, and, P. Kielanowski, Lecture Notes in Physics Vol. 504 (Springer, Berlin, 1998), p. 181;
21. A. Bohm, Adv. Chem. Phys. ADCPAA 0065-2385 122, 301 (2002);
22. A. Bohm, Fortschr. Phys. FPYKA6 0015-8208 10.1002/prop.200310073 51, 551 (2003).
23. I. Prigogine, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua. 560530115 53, 105 (1995).
24. E. C. G. Sudarshan, C. B. Chiu, and G. Bhamathi, Adv. Chem. Phys. ADCPAA 0065-2385 99, 121 (1997).
25. C. A. Nicolaides, in Irreversible Quantum Dynamics, edited by, F. Benatti, and, R. Floreanini, Lecture Notes in Physics Vol. 622 (Springer, Berlin, 2003), p. 357;
26. C. A. Nicolaides and D. R. Beck, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.560140411 14, 457 (1978);
27. C. A. Nicolaides, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.10186 89, 94 (2002), and references therein.
28. N. Moiseyev and M. Lein, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp034390y 107, 7181 (2003).
29. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965).
30. N. Moiseyev and S. Friedland, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.441624 74, 4739 (1981).
31. E. Narevicius and N. Moiseyev, Adv. Topics Theor. Chem. Phys. 12, 311 (2003).
32. H. Barkay and N. Moiseyev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.044702 64, 044702 (2001).
33. H. Feshbach, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(58) 90007-1 5, 357 (1958);
34. Theoretical Nuclear Physics (Wiley, New York, 1992).
35. N. Moiseyev and J. O. Hirschfelder, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.454275 88, 1063 (1998).
36. N. Moiseyev, P. R. Certain, and F. Weinhold, Mol. Phys. MOPHAM 0026-8976 36, 1613 (1978);
37. N. Lipkin, N. Moiseyev, and E. BrEndas, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.549 40, 549 (1989);
38. N. Moiseyev, Mol. Phys. MOPHAM 0026-8976 47, 585 (1982);
39. H. J. Korsch, H. Laurent, and R. b6hlenkamp, Mol. Phys. MOPHAM 0026-8976, 43, 1441 (1981);
40. M. Rittby, N. Elander, and E. BrEndas, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.24.1636 24, 1636 (1981).
41. E. Persson, T. Gorin, and I. Rotter, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.3339 54, 3339 (1996).