The Importance of the Domain of Operators in Quantum Mechanics

Doliat, M.; Parviz, N.

doi:10.30511/ttmp.2024.2023459.1022

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