Fractional quantum eulercauchy equation in the schrödinger picture, complexified harmonic oscillators and emergence of complexified lagrangian and hamiltonian dynamics

Modern Physics Letters B

Volumn 23, Issue 28, 2009, Pages 3369-3386

  El Nabulsi, Ahmad Rami ^a  

^a Jeju National University   (South Korea)

Author keywords

Complexified dynamics; Fractional action like variational approach; Fractional EulerLagrange equations; Fractional Schr dinger equation

Indexed keywords

EID: 70450162817     PISSN: 02179849     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217984909021387     Document Type: Article

References (65)

1. H. Dekker, Phys. Rep. 80(1) (1981) 1.
2. H. Dekker, Phys. Rev. A 16(5) (1977) 2126.
3. H. Feshbach and Y. Tikochinsky, N. Y. Acad. Sci. 38(II) (1977) 44.
4. H. Gzly, Phys. Rev. A 27(5) (1983) 2297.
5. C. Um, K. Yeon and T. F. George, Phys. Rep. 362 (2002) 63.
6. H. Bateman, Phys. Rev. 38 (1931) 815.
7. P. Caldirola, Nuovo Cimento 18 (1941) 393.
8. E. Kanai, Prog. Theor. Phys. 3(440) (1948).
9. I. A. Pedrosa and I. Guedes, Quantum states of generalized time-dependent invertor harmonic oscillator, arxiv:quant-ph/0307084v1.
10. N. Eti, Classical and Quantum Euler Equation, MS Thesis, Izmir (2007) June.
11. K. H. Yeon and C. I. Um, J. Korean Phys. Soc. 24(5) (1991) 369.
12. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), and therein.
13. N. A. Chernikov and E. A. Tagirov, Ann. Inst. H. Poincaré A (N:S:) 9 (1968) 109.
14. D. Gomes and E. Capelas De Oliveira, IJMMS 69 (2004) 3775.
15. R. A. El-Nabulsi, Int. J. Mod. Phys. B 23(16) (2009) 3349.
16. K. B. Oldham and J. Spanier, The Fractional Calculus (Academy Press, New York, London, 1974).
17. S. Samko, A. Kilbas and O. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach, New York, 1993).
18. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Di rential Equations (John Wiley & Sons Inc., New York, 1993).
19. I. Podlubny, An Introduction to Fractional Derivatives, Fractional Di rential Equations, to Methods of Their Solution and Some of Their Applications (Academic Press, New York-London, 1999).
20. R. Hilfer (ed.), Applications of Fractional Calculus in Physics (World Scientic, New Jersey, London, Hong Kong, 2000).
21. J. A. Tenreiro Machado (ed.), Nonlin. Dynam. 29(1{4) (2002).
22. M. D. Ortigueira and J. A. Tenreiro Machado (eds.), Signal Process. 83(11) (2003) 2285.
23. O. P. Agrawal, J. A. Tenreiro Machado and J. Sabatier (eds.), Nonlin. Dynam. 38(1{4) (2004) 481-489.
24. M. D. Ortigueira and J. A. Tenreiro Machado (eds.), Signal Process. 86(10) (2006) 2503.
25. M. D. Ortigueira and J. A. Tenreiro Machado (eds.), J. Vibr. Contr. 14(9{10) (2008) 1253.
26. J. A. Tenreiro Machado and A. Luo (eds.), ASME J. Comput. Nonlin. Dynam. 3(2) (2008).
27. R. A. El-Nabulsi, Fizika A 14(4) (2005) 289.
28. R. A. El-Nabulsi, Int. J. Appl. Math. 17 (2005) 299.
29. R. A. El-Nabulsi and D. F. M. Torres, J. Math. Phys. 49 (2008) 053521.
30. R. A. El-Nabulsi and D. F. M. Torres, Math. Meth. Appl. Sci. 30(15) (2007) 1931.
31. R. A. El-Nabulsi, Int. J. Mod. Geom. Meth. Mod. Phys. 5(6) (2008) 863, and therein.
32. R. A. El-Nabulsi, Int. J. Geom. Meth. Mod. Phys. 6(1) (2009).
33. R. A. El-Nabulsi, Chaos, Solitons & Fractals 42(1) (2009) 52.
34. R. A. El-Nabulsi, Chaos, Solitons & Fractals 42(1) (2009) 84.
35. R. A. El-Nabulsi, Chaos, Solitons & Fractals 41(5) (2009) 2262.
36. R. A. El-Nabulsi, Chaos, Solitons & Fractals 42(4) (2009) 2384.
37. R. A. El-Nabulsi, Int. J. Appl. Math. & Statistics 5(S06) (2006) 50.
38. R. A. El-Nabulsi, Fizika B 17(3) (2008) 369.
39. R. A. El-Nabulsi, Fizika A 17(2) (2008) 71.
40. G. S. F. Frederico and D. F. M. Torres, Int. J. Ecol. Econ. Stat. 9 (2007) 74.
41. A. Valtakoski, Mathematical aspects of functional integration, Helsingin Yliopisto Fysiikan Laitos Teoreettisen Fysiikan Osasto Pl 9 (Siltavuorenpenger 20 D) 00014 Helsingin Yliopisto (2000).
42. F. J. Bloore, L. Routh and J. Underhill, Nucl. Phys. B 55(2) (1973) 637.
43. B. G. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, UK).
44. X. Ma and C. M. Soukoulis, Phys. B: Conden. Matt. 296(1{3) (2001) 107.
45. U. Peskin and N. Moiseyev, J. Chem. Phys. 99(6) (1993) 4590.
46. H. Sambe, Phys. Rev. A 7 (1973) 2203.
47. J. S. Howland, Math. Ann. 207 (1974) 315.
48. J. S. Howland, Indiana Univ. Math. J. 28 (1979) 471.
49. C. Besse, Articial boundary conditions for the Schrodinger equation with external potential, in 2nd Canada-France Congress, June 1{5 (2008), Universite de Quebec a Montreal, Variational and Numerical Methods in Geometry, Physics and Chemistry, Org: Lia Bronsard (McMaster), Eric Cances (ENPC) and Maria J. Esteban (CNRSParis Dauphine).
50. C. M. Bender, D. D. Holm and D. W. Hook, Complexied Dynamical Systems, hepth/ 0705.3893.
51. K. Fujikawa and H. Suzuki, Path Integrals and Quantum Anomalies (Oxford University Press, USA, 2004).
52. S. Ghosh and S. K. Modak, Classical oscillator with position-dependent mass in a complex domain, math-ph/0803.2531 and therein.
53. V. I. Sbitnev, Bohmian trajectories and the path integral paradigm. Complexied Lagrangian mechanics, arXiv:0808.1245.
54. G. Guralnik and C. Pehlevan, Complex Langevin equations and Schwinger{Dyson equations, hep-th/0710.3756.
55. G. Guralnik and C. Pehlevan, Complexied path integrals and the phases of quantum eld theory, hep-th/0710.1256.
56. C.-C. Chou and R. E. Wyatt, Phys. Rev. A 76 (2007) 012115.
57. L. L. Salcedo, J. Math. Phys. 38 (1997) 1710.
58. L. L. Salcedo, J. Phys. A: Math. Gen. 40 (2007) 9399.
59. H. Okamoto, K. Okano, L. Schulke and S. Tanaka, Nucl. Phys. B 324 (1989) 684.
60. H. W. Hamber and H. C. Ren, Phys. Lett. B 159 (1985) 330.
61. J. Flower, S. W. Otto and S. Callahan, Phys. Rev. D 34(2) (1986) 598.
62. M. S. El Naschie, Chaos Solitons & Fractals 5(6) (1995) 1031.
63. M. S. El Naschie, Chaos Solitons & Fractals 11 (2000) 1149.
64. A. R. El-Nabulsi and H. J. Lee, Int. J. Appl. Math. 18(3) (2005) 355.
65. A. Sym, J. Nonlin. Math. Phys. 12(1) (2005) 648.