论文标题
波功能的刚度，可分离性和尖端条件
Rigidity, separability, and cusp conditions of a wave function
论文作者
论文摘要
我们在量子力学中介绍\ textit {刚性}的概念，以及一个波函数的\ textit {pinned point}的概念。固定点的概念是对振动字符串描述中熟悉的概念的概括，而引入了刚性的概念来描述波函数对能量，电位和/或外部扰动变化的敏感性。通过这些概念及其数学含义，我们介绍并制定了尖峰条件，并且尖端作为具有$ n \ ge 2 $的任意$ n $ body量子系统的基本特性，从而将其相关性大大扩展到了库仑系统之外。该理论对任意$ n $体量子系统的严格约束提供了严格的约束，特别是在其短距离对相关性上，这对于更好地理解强相关系统至关重要。更广泛地说，此处介绍的理论和派生是重建了$ n $体量子理论的数学和概念基础的一部分，并结合了以前隐藏的属性和通过刚性概念和固定点所揭示的见解。它包括2体波函数与能量的一般分析特性及其与尖端条件和尖端功能的关系。它包括严格的派生和在$（n> 2）$ - 身体量子系统中的2粒子可分离性及其与尖cusp条件的关系中的2粒子可分离性的理解。它还基于其短距离相关性的普遍行为，包括2体和$ n $体的量子系统的分类。
We introduce in quantum mechanics a concept of \textit{rigidity} and a concept of a \textit{pinned point} of a wave function. The concept of a pinned point is a generalization of a familiar concept in the description of a vibrating string, while the concept of rigidity is introduced to describe the sensitivity of a wave function to changes in energy, potential, and/or external perturbation. Through these concepts and their mathematical implications, we introduce and formulate cusp conditions and cusp functions as fundamental properties of an arbitrary $N$-body quantum system with $N\ge 2$, greatly expanding their relevance beyond the Coulombic systems. The theory provides rigorous constraints on an arbitrary $N$-body quantum system, specifically on its short-range pair correlation that is essential to a better understanding of strongly correlated systems. More broadly, the theory and the derivations presented here are part of a reconstruction of the mathematical and conceptual foundation of an $N$-body quantum theory, incorporating previously hidden properties and insights revealed through the concepts of rigidity and pinned points. It includes general analytic properties of a 2-body wave function versus energy and their relations to cusp conditions and cusp functions. It includes a rigorous derivation and an understanding, in terms of an emergent length scale, of the 2-particle separability in an $(N>2)$-body quantum system and its relations to cusp conditions. It also includes a classification of quantum systems, both 2-body and $N$-body, based on the universal behaviors in their short-range correlation.
