Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

The Importance of the Domain of Operators in Quantum Mechanics

Document Type : Original Article

Authors
M. Doliat 1
N. Parviz 2
1 Department of Physical Chemistry and Nano chemistry, Faculty of Chemistry, Alzahra University, P.O. Box: 1993893973 Tehran, Iran
2 Department of Physical Chemistry and Nano Chemistry, Faculty of Chemistry, Alzahra University
10.30511/ttmp.2024.2023459.1022
Abstract
This paper aims to examine the significance of the domain of operators in the mathematical and physical structure of quantum mechanics. Specifically, we explore the distinction between observable self-adjoint and Hermitian operators, determined by their respective domains. We also discuss the Algebra of unbounded operators with the concept of the domain of operators. Our analysis reveals that creation and annihilation operators are not generally self-adjoint towards each other in standard quantum mechanics, as demonstrated through mathematical equations.
Keywords
Unbouded operator
Bounded operator
Hermitian operator
Self-adjoint operator
Subjects
1. W. Pauli, General Principles of Quantum Mechanics
(Springer Verlag, New York, 1980)#

2. B. C. Hall, Quantum Theory For Mathematics (GTM,
Springer, 2013)#

3. M. Jafari  Matehkolaee, A. Hajimohamadi Fariman,
T.Theo. Math. Phy 1, 1 (2024)#

4. K. Schmudgen, Unbounded self-adjoint operators on
Hilbert space (Springer, 2012).#

5. G. Teschi, Mathematical Methods In Quantum Mechan
ics, with applications to Schrodinger operators, 2ed
(American Mathematical Society, 2014)#

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

7. J. Weidmann, Linear operators in Hilbert Spaces
(Springer Verlag, New York, 1980)#

8. N. I. Akhiezer, I. M. Glazman,  Theory of Linear opera
tors in Hilbert Spaces  (Pitman, London, Vol I, 1981)#

9. M. Jafari Matehkolaee, Pramana J.Phys. 93, 84 (2019)#
 
Transactions in Theoretical and Mathematical Physics
Volume 1, Issue 2
Spring 2024
Pages 46-49

  • Receive Date 20 February 2024
  • Revise Date 26 April 2024
  • Accept Date 27 April 2024
  • First Publish Date 01 May 2024
  • Publish Date 01 May 2024