Development of Algorithms for the Manipulation of Non-commutative Structures in Quantum Theory

Authors

Mark Transtrum, Brigham Young University
Dr. Jean-Francois Van Huele, Brigham Young University

Keywords

algorithms, non-commutative structures, quantum theory

College

Physical and Mathematical Sciences

Department

Physics and Astronomy

Abstract

Quantum mechanics is one of the fundamental theories of physics. Its formal mathematical description is marked by the appearance of non-commutative operators. The non-commutativity provides a rich mathematical language appropriate for describing quantum theory. The commutator of two operators is defined as the difference between the product of the two operators and the product in reverse order. The commutator plays a foundational role in the theory of quantum mechanics. For example, in the Heisenberg picture, the time evolution of an operator is determined by its commutator with the Hamiltonian operator. Also, normal ordering (an important problem in quantum optics) is achieved by repeated application of the definition of the commutator.

Recommended Citation

Transtrum, Mark and Van Huele, Dr. Jean-Francois (2013) "Development of Algorithms for the Manipulation of Non-commutative Structures in Quantum Theory," Journal of Undergraduate Research: Vol. 2013: Iss. 1, Article 2731.
Available at: https://scholarsarchive.byu.edu/jur/vol2013/iss1/2731