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arXiv · 2003.11472

Fundamentals of Quantum Mechanics in Liouville Space

Jerryman A. Gyamfi
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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 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.

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Jerryman A. Gyamfi. 2020-11-18. Fundamentals of Quantum Mechanics in Liouville Space. https://doi.org/10.1088/1361-6404%2Fab9fdd

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