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 wants 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.

中文翻译：

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刘维尔空间中的量子力学基础

本文的目的是基于 Kronecker 乘积和我们称为“bra-flipper”算子的使用，阐明在任何有限维 Liouville 空间中进行量子力学的连贯且易于理解的方法。这里阐述的形式主义的一大优势是它与狄拉克的括号符号有着惊人的相似之处。为了说明如何有效地使用形式主义，我们用它来求解两能级量子系统的量子光学主方程，并找到它的克劳斯算子和表示。本文面向希望对 Liouville 空间形式主义有更深入了解的具有线性代数基础知识的学生和研究人员。