Quantization of nonconservative systems using fractional calculus

WSEAS Transactions on Mathematics

Volumn 5, Issue 7, 2006, Pages 853-863

  Rabei, Eqab M ^a,b   Ajlouni, Abdul Wali ^c   Ghassib, Humam B ^c  

^a JERASH UNIVERSITY   (Jordan)

^b MUTAH UNIVERSITY   (Jordan)

^c UNIVERSITY OF JORDAN   (Jordan)

Author keywords

Canonical quantization; Fractional calculus; Hamiltonian formulation; Non conservative systems

Indexed keywords

EQUATIONS OF MOTION; HAMILTONIANS; LAGRANGE MULTIPLIERS; MATHEMATICAL OPERATORS;

CANONICAL CONJUGATE-MOMENTUM COORDINATES; CANONICAL QUANTIZATION; DIRAC METHOD; FRACTIONAL CALCULUS; HEISENBERG EQUATION; NON-CONSERVATIVE SYSTEMS; POISSON-BRACKET RELATIONS;

MATHEMATICAL MODELS;

EID: 33745486529     PISSN: 11092769     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. H. Goldstein, Classical Mechanics (2nd ed., Addison-Wesley, 1980).
2. F. Riewe, Physical Review E 53,1890 (1996).
3. F. Riewe, Physical Review E 55,3581 (1997).
4. E. M. Rabei, T. Al-halholy and A. Rousan, Potentials of Arbitrary Forces with Fractional Derivatives. Accepted for publication, International Journal of Modern Physics A (2004). w York, 1970).
5. K. Hajra, Stochastic Equation of a Dissipative Dynamical Systems and its Hydrodynamical Interpretation, Journal of Mathematical Physics. 32,1505 (1991).
6. B. Oldham and J. Spanier, The Fractional Calculus (Academic Press, NewYork, 1974).
7. A. Carpintri and F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics (Springer, New York, 1997).
8. D.W. Dreisigmeyer and M. Young, Journal of Physics A: Mathematical and General 36, 8279 (2003).
9. D. W. Dreisigmeyer, and M. Young, http://www.arXiv:physics/0312085 vl(2003).
10. O.P. Agrawal, Journal of Mathematical Analysis and Applications 272, 368 (2002).
11. P. A. M. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School of Science, Yeshiva University, New York, 1964).
12. B. M. Pimental and R. G. Teixeira, arXiv:hep-/9704088 vl (1997).
13. P.T.Matthews, Introduction to Quantum Mechanics (2nd ed., McGraw-Hill Ltd., London, 1974).
14. J. J. Sakurai, Modern Quantum Mechanics (Benjamin/Cummings, Menlo Park, CA, 1985).
15. D. J. Griffiths, Introduction to Quantum Mechanics (Prentice-Hall, New Jersey, 1995).
16. E. Merzbacher, Quantum Mechanics (Wiley,New York, 1970)