Fundamentals of quantum mechanics in Liouville space

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 e...

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Bibliographic Details
Published inEuropean journal of physics Vol. 41; no. 6; pp. 63002 - 63061
Main Author Gyamfi, Jerryman A
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.11.2020
Subjects
bra-flipper operator
Hilbert space
Kronecker product
Liouville space
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Summary: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.
Bibliography:EJP-105291.R2
ISSN:0143-0807
1361-6404
DOI:10.1088/1361-6404/ab9fdd