物理
厄米矩阵
哈密顿量(控制论)
转置
单一制国家
复共轭
量子力学
数学物理
公理
理论物理学
量子
量子力学的数学表述
对称(几何)
经典力学
开放量子系统
量子操作
特征向量
数学分析
数学
几何学
数学优化
法学
政治学
标识
DOI:10.1088/0034-4885/70/6/r03
摘要
The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that time evolution is unitary (probability-preserving). This paper describes an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose +complex conjugate) is replaced by the physically transparent condition of space–time reflection ( ) symmetry. If H has an unbroken symmetry, then the spectrum is real. Examples of -symmetric non-Hermitian quantum-mechanical Hamiltonians are and . Amazingly, the energy levels of these Hamiltonians are all real and positive!
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