希尔伯特空间中的概率流和概率守恒

PROBABILITY CURRENTS AND CONSERVATION OF PROBABILITY IN HILBERT SPACE

实空间中的概率流概念和概率守恒定理被推广到希尔伯特 (Hilbert)状态空间 ,从而得到了概率流算符的通式 .应用一般形式的概率流算符公式 ,还导出了紧束缚模型中单电子和互作用多电子系统的概率流算符 ,并以异常简单的方式证明了反射

The general formula of probability current operator is obtained by generalizing the concept of probability current and the theorem of probability conservation. With the help of this new formula, we derive a probability current operator for the tight-binding models of single electron system and interacting-multi-electron system, and then prove, in a very simple way, the normalization condition of reflection-transmission currents.