标题： PT对称量子系统的格拉姆矩阵 显示英文标题

标题： The Gram Matrix of a PT-symmetric Quantum System

摘要： 对可对角化的PT对称哈密顿量的本征态满足非传统的完备性和正交性关系。 这些关系反映了与非厄米可对角化算符相关的双正交基对的性质。 类似地，这种基对在PT对称存在的情况下，表现出一种特定结构的Gram矩阵：其逆矩阵通过简单地改变某些矩阵元素的符号即可得到。 显示英文摘要

摘要： The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy unconventional completeness and orthonormality relations. These relations reflect the properties of a pair of bi-orthonormal bases associated with non-hermitean diagonalizable operators. In a similar vein, such a dual pair of bases is shown to possess, in the presence of PT symmetry, a Gram matrix of a particular structure: its inverse is obtained by simply swapping the signs of some its matrix elements.