Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

A new approach to momentum operators in curved space

Document Type : Original Article

Authors
M. Jafari Matehkolaee 1
Z. Norouzbeh 2
1 Department of Physics, Amirkabir University of Technology (Tehran Polytechnic ), P.O.Box: 15875-4413,Tehran, Iran
2 Department of physics, Alzahra University, Tehran, Iran
10.30511/ttmp.2024.2006716.1011
Abstract
In this paper we have obtained momentum representation in curved space with a different procedure to previous reports and then as a straight application for these operators we have investigated them on the compact manifold as a sphere. Our investigation indicates the spectrum of generalized momentum operators on the compact manifold is discrete.

In this paper we have obtained momentum representation in curved space with a different procedure to previous reports and then as a straight application for these operators we have investigated them on the compact manifold as a sphere. Our investigation indicates the spectrum of generalized momentum operators on the compact manifold is discrete.

In this paper we have obtained momentum representation in curved space with a different procedure to previous reports and then as a straight application for these operators we have investigated them on the compact manifold as a sphere. Our investigation indicates the spectrum of generalized momentum operators on the compact manifold is discrete.
Keywords
Generalized momentum operators
Riemannian manifold
Quantum mechanics on the sphere
Subjects
1. L. Viola, R. Onofrio, Phys. Rev. D 55, (1996)#

2. J. F. Doonoghue and B. R. Holstein, Am. J. Phys. 54, 9
Phys. 11, 8 (2014)#
3. Y. Q. Cai, G. Papini, Gen. rel. Grav. 22, 3 (1990)#
4. A. Karamatskou, H. Klinert, Int. J. Geom. Methods.#

5. C. C. Barros Jr, Eur. Phys. J. C 42 (2005)#

6. W. Pauli, General Principles of Quantum Mechanics,
(Springer – Verlag, New York, 1980)#

7. B. S. DeWitt, T. Stanev, Phys. Rev. 85, 653 (1952)#

8. M. Carreau, Phys. Rev. D 40, 6 (1989)#

9. C. S. Wang, Am. J. Phys. 57, 1 (1989)#

10. P. V. Gonzalez, J. C. Parra, Am. J. Phys. 49, 8 (1981)#

11. B. Leaf, Am. J. Phys. A 47, 9 (1979)#

12. M. Jafari Matehkolaee, Pramana J. Phys. 93, 84 (2019)#

13. L Jahangiri, H. Panahi, Ann. Phys. 375 (2016)#

14. K. Kowalski, J. Rembielinski, J. Phys. A. 33 (2000)#

15. M. Jafari Matehkolaee, Pramana J. Phys. 95, 131(2021)#

16. G. R. Gruber, Found. Phys. 6, 1 (1976).#

17. J. M. Domingos, M. H. Caldeira, Found. Phys.  14, 7
(1984)#

18. I. Rigas, L. L. Sanchez-Soto, A. B. Klimov, J.
Rhehacek, Z. Hradil, Ann. Phys. 326, 426 (2011)#
 
 
Transactions in Theoretical and Mathematical Physics
Volume 1, Issue 2
Spring 2024
Pages 39-42

  • Receive Date 11 July 2023
  • Revise Date 29 November 2023
  • Accept Date 10 February 2024
  • First Publish Date 10 February 2024
  • Publish Date 01 May 2024