Spin Operators, Pauli Group, Commutators, Anti-Commutators, Kronecker Product and Applications
Willi-Hans Steeb, Yorick Hardy
TL;DR
This paper explores mathematical properties of Pauli spin matrices, the Pauli group, and related operators, applying them to various quantum mechanics problems including eigenvalues, spin Hamiltonians, and basis constructions.
Contribution
It provides a comprehensive study of Pauli matrices, their algebraic structures, and diverse applications in quantum physics, including eigenvalue solutions and basis design.
Findings
Eigenvalue problems solved using Pauli matrices
Exponential functions of spin matrices analyzed
Applications to quantum basis and operator constructions
Abstract
Pauli spin matrices, Pauli group, commutators, anti-commutators and the Kronecker product are studied. Applications to eigenvalue problems, exponential functions of such matrices, spin Hamilton operators, mutually unbiased bases, Fermi operators and Bose operators are provided.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · graph theory and CDMA systems