量子力学的数学新视角  

A New Mathematical Perspective of Quantum Mechanics

作　　者：陈木法 CHEN Mu-Fa(Research Institute of Mathematical Science,Jiangsu Normal University,Xuzhou,Jiangsu,221116,P.R.China;School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems(Ministry of Education),Beijing Normal University,Beijing,100875,P.R.China)

机构地区：[1]江苏师范大学数学研究院,徐州江苏221116 [2]北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京100875

出　　处：《数学进展》2021年第3期321-334,共14页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11771046,12090011);国家重点研发计划(No.2020YFA0712900);教育“双一流”建设学科和江苏高校优势学科建设工程。

摘　　要：在研究算法时遇到如下问题:除实对称矩阵或复厄米矩阵外,何种更大的矩阵类具有实谱?后者是量子力学的两大特征之一,另一特征是波动性.闻名于世的量子力学的"百年大战"就是围绕着波动方程的解是否存在"随机性"展开的.我们将介绍这几年的探索,以一个意外结果打开了一个新视角.须知,现代数学的多个分支源于量子力学.可以想象,新视角所触及的决非仅仅几个小课题.In the study of the algorithm,we encounter the following problems:besides the real symmetric matrices or complex Hermite ones,what is the larger class of matrices having real spectrum?The latter is one of the two characteristics of quantum mechanics;the other one is the volatility.The well-known "centennial war"is about whether the solution of wave equation exists "randomness".We will introduce the explorations of the past few years with an unexpected result.It should be noted that many branches of modern mathematics originate from quantum mechanics.It can be imagined that the new perspective touches on more than just a few small topics.

关 键 词：统计物理 量子力学 可厄米矩阵 新谱论 

分 类 号：O413.1[理学—理论物理] O411.1[理学—物理]