论文标题
具有正确定度量的非螺旋岩系统的操纵希尔伯特空间方法
Rigged Hilbert Space Approach for Non-Hermite Systems with Positive Definite Metric
论文作者
论文摘要
我们研究了基于索具的希尔伯特空间的乳房bra-ket形式主义，该空间用于具有正定度度的非含量量子系统。首先，建立了以正定指标为特征的操纵的希尔伯特空间。借助核光谱定理用于获得的索具希尔伯特空间，准甲层操作员的广义特征向量显示了胸罩的光谱膨胀。光谱膨胀被用来赋予完整的双向异常系统以及赫米特和非铁矿系统之间的转换理论。作为应用的一个例子，我们展示了对某些平均时间对称量子系统的操纵希尔伯特太空处理的具体描述。
We investigate Dirac's bra-ket formalism based on a rigged Hilbert space for a non-Hermite quantum system with a positive-definite metric. First, the rigged Hilbert space, characterized by positive-definite metric, is established. With the aid of the nuclear spectral theorem for the obtained rigged Hilbert space, spectral expansions are shown for the bra-kets by the generalized eigenvectors of a quasi-Hermite operator. The spectral expansions are utilized to endow the complete bi-orthogonal system and the transformation theory between the Hermite and non-Hermite systems. As an example of application, we show a specific description of our rigged Hilbert space treatment for some parity-time symmetrical quantum systems.
