论文标题
liouville空间中量子力学的基本原理
Fundamentals of Quantum Mechanics in Liouville Space
论文作者
论文摘要
本文的目的是根据使用Kronecker产品以及我们所说的“ Bra-Flipper”操作员，表达在任何有限维的Liouville空间中进行量子力学的连贯且易于理解的方式。这里揭示的形式主义的更大优势之一是它与迪拉克的胸罩符号所具有的惊人相似之处。为了说明如何有效地采用形式主义，我们使用它来解决两级量子系统的量子光学主方程，并找到其kraus ocerator ocerator sugy表示。该论文是向学生和研究人员介绍的，具有一些线性代数的基本知识，他们想深入了解liouville太空形式主义。传达了这些概念，以便将形式主义的应用到量子物理学中更复杂的问题中，直接且无限制。
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.
