2020/03/31 by Jerryman A. Gyamfi, Jerryman A Gyamfi
Mathematics · Physics and Astronomy · #Formalism (music) #Interpretations of quantum mechanics #Kronecker delta #Kronecker product #Open quantum system #Operator (biology) #Operator algebra #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Quantum process #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1361-6404/ab9fdd
published as Eur. J. Phys. 41 063002 (2020) · 60 pages, 1 table
openalex created_date 2020/04/03 · openalex publication_date 2020/07/08 · arxiv created 2020/11/18 · arxiv updated 2020/11/19 · openalex updated_date 2026/08/05
Abstract The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of a Kronecker product and what we have termed the ‘bra-flipper’ operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac’s bra-ket notation. For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system and find its Kraus operator sum representation. The paper is addressed to students and researchers with some basic knowledge of linear algebra who want to acquire a deeper understanding of the Liouville space formalism. The concepts are conveyed so as to make the application of the formalism to more complex problems in quantum physics straightforward and unencumbered.