Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Concept of weak derivative by resorting physical examples

Document Type : Original Article

Authors
1 Department of Physics, Amirkabir University of Technology (Tehran Polytechnic ), P.O.Box: 15875-4413,Tehran, Iran
2 Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
Abstract
In this article, we endeavor to present the concept of weak derivatives with respect to the potential of a charge distribution. Furthermore, in quantum mechanics the correct momentum operators which are self-adjoint can be defined by weak derivative
Keywords
Subjects

1. J. Jost, Postmodern Analysis (Springer, Berlin, Heidel
berg, 1998)#

2. W. P. Ziemer, Weakly Differentiable Functions
(Springer, 1989)#

3. A. K. Nandakumaran, P. S. Datti, Partial Differential
Equations, Classical Theory with a Modern touch
(Cambridge University Press, 2020)#

4. J.  P. Gossez, Bull. de la Classe des sc. 67 (1981)#

5. B. Heidergott and X. R. Cao, IEEE Trans. Automat.
Contr. 47, 7  (2002)#

6. A. Eikmier, E. Emmerich, E. Schöll, Int. J. Dynam.
Control, 6  (2018)#

7. G. B. Lieberman, Oblique Derivative Problems for
Elliptic Equations (World Scientific, 2013)#

8. P. A. M. Dirac, The Principle of quantum mechanics,
Fourth Edition (Oxford university press, 1957)#

9. Q. Teschi, Mathematical methods in Quantum mechan
ics, with applications to Schrödinger operators  (Amer
ican Mathematical Society, 2014)#

10. F. Gieres, Rep. . Prog. in Phy. 63, 12 (2001).#

11. M. Valter, Int. J. Geom. Meth. Mod. Phys. 13 (2016)#

12. H Brezis, Functional analysis, Sobolev spaces and
partial differential equations (Springer, 2011).#

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

14. M. Jafari Matehkolaee, Z. Norouzbeh, Trans. Th.
Math. Phy. 1, (2) 2024#
 
Volume 1, Issue 3
Summer 2024
Pages 68-71

  • Receive Date 15 April 2024
  • Revise Date 26 April 2024
  • Accept Date 01 May 2024
  • First Publish Date 01 August 2024
  • Publish Date 01 August 2024