Subscribe Now Subscribe Today
Research Article

Particle in a Finite Potential Well, with Dissipation

O. Abu-Haija , A. A. Mahasneh , Ali Taani and A-W. Ajloun
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail

In this study fractional derivatives have been used to study a nonconservative system: free particle in a finite potential well, containing a dissipative medium. The Lagrangian and other classical functions have been introduced to take into account nonconservative effects. The canonical quantization of the system is carried out according to the Dirac method. A suitable Schrodinger equation is set up and solved for the Lagrangian representing this system.

Related Articles in ASCI
Similar Articles in this Journal
Search in Google Scholar
View Citation
Report Citation

  How to cite this article:

O. Abu-Haija , A. A. Mahasneh , Ali Taani and A-W. Ajloun , 2007. Particle in a Finite Potential Well, with Dissipation. Journal of Applied Sciences, 7: 1669-1673.

DOI: 10.3923/jas.2007.1669.1673


1:  Agrawal, O.P., 2001. Formulation of euler-lagrange equations for fractional variational problems. J. Math. Anal. Appli., 272: 368-379.
Direct Link  |  

2:  Arfken, G., 1985. Mathematical Methods for Physical Sciences. Academic Press, Orlando, Florida.

3:  Carpintri, A. and F. Mainardi, 1997. Fractals and Fractional Calculus in Continuum Mechanics. Springer, New York.

4:  Dass, T. and S. Sharma, 1998. Mathematical Methods in Classical and Quantum Physics. 1st Edn., University Press, Hayderabad, India, ISBN: 978-81-7371-089-6.

5:  Dirac, P.A.M., 1964. Lectures on Quantum Mechanics. Belfer Graduate School of Science. Yeshiva University, New York.

6:  Dreisigmeyer, D.W. and M. Young, 2003. Nonconservative lagrangian mechanics: A generalized function approach. J. Phys. A: Math. General, 36: 8297-8310.
Direct Link  |  

7:  Goldstein, H., 1980. Classical Mechanics. 2nd Edn., Addison-Wesley, New York.

8:  Griffiths, D.J., 1995. Introduction to Quantum Mechanics. Prentice-Hall, New Jersey.

9:  Merzbacher, E., 1970. Quantum Mechanics. Wiley, New York.

10:  Oldham, K.B. and J. Spanier, 1974. The Fractional Calculus. 1st Edn., Academic Press, New York.

11:  Pimental, B.M. and R.G. Teixeira, 1997. Generalization of the hamilton-jacobi approach for higher order singular systems. Arxiv preprint hep-th/9704088 vl,.

12:  Rabei, E.M., T. Al-Halholy and A. Rousan, 2004. Potentials of arbitrary forces with fractional derivatives. Int. J. Modern Phys. A, 19: 3083-3092.
Direct Link  |  

13:  Rabei, E., A.W. Ajlouni and H. Ghassib, 2006. Quantization with fractional calculus. Wseas Trans. Math., 5: 853-864.

14:  Rabei, E., A.W. Ajlouni and H. Ghassib, 2006. Quantization of non-conservative systems. Proceedings of the 9th WSEAS International Conference on Applied Mathematics (MATH'06), Math, Tele-Info and SIP '06, May 27-29, Istanbul, Turkey.

15:  Riewe, F., 1996. Nonconservative lagrangian and hamiltonian mechanics. Phys. Rev., E, 53: 1890-1899.
Direct Link  |  

16:  Riewe, F., 1997. Mechanics with fractional derivatives. Phys. Rev. E, 55: 3581-3592.
Direct Link  |  

©  2021 Science Alert. All Rights Reserved