Journal of Applied Mathematics and Physics, 2021, 9, 856-863
https://www.scirp.org/journal/jamp
ISSN Online: 2327-4379
ISSN Print: 2327-4352
DOI: 10.4236/jamp.2021.95058 May 14, 2021 856 Journal of Applied Mathematics and Physics
The Quantum Mechanical Rotation Operators
of Spins 5/2 to 7/2
Mehpeyker Kocakoç
1
, Recep Tapramaz
2
1
Department of Computer Technologies, Vocational School of İmamoğlu, Çukurova University, Adana, Turkey
2
Department of Physics, Ondokuz Mayıs University, Samsun, Turkey
Abstract
With the creation of logic gates and algorithms for quantum computers and
entering our lives, it is predicted that great developments will take place in
this area and important efforts are made. Spin rotation processors are quan-
tum mechanical rotation processors and have no classic counterparts. The
rotation operators of spin 1/2 are well known and can be found in related
textbooks. But rotation operators of other spins greater than 1/2 can be found
numerically by evaluating the series expansions of exponential operator ob-
tained from Schrödinger equation, by evaluation of Wigner-d formula or by
recently established expressions in polynomial forms discussed in the text. In
a previous paper, rotation operators for spins 1/2 to 2 were published. In this
work, explicit symbolic expressions of x, y and z components of rotation op-
erators for spin 5/2, 3 and 7/2 are worked via exponential operator for each
element of related spin operators and utilizing simple linear curve fitting
process. The procedures gave out exact expressions of each element of the
rotation operators.
Keywords
Rotation Operator, Quantum Information Systems, Spin, Electron
Paramagnetic Resonance (EPR)
1. Introduction
Quantum mechanical rotation operators in explicit forms are the essential tools
of microscopic systems. Wigner [1] introduced expressions of rotation matrices
or Wigner-d matrices for orbital angular momenta with the basis of standard
Euler angles. Real rotation operators for total angular momenta of 1/2, 1, 3/2 and
2 were generated from Wigner-d formula in some classical textbooks of quan-
tum mechanics [2]-[8]. A recently published paper on rotation operators by
How to cite this paper: Kocakoç, M. and
Tapramaz, R. (2021) The Quantum Me-
chanical Rotation Operators of Spins 5/2 to
7/2. Journal of Applied Mathematics and
Physics, 9, 856-863.
https://doi.org/10.4236/jamp.2021.95058
Received: December 25, 2020
Accepted: May 11, 2021
Published: May 14, 2021
Copyright © 2021 by author(s) and
Scientific Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY 4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access