量子可观测量作为Fréchet灵敏度核
Quantum observables as Fréchet sensitivity kernels
浏览论文内容
中文总结 AI 辅助
该研究提出量子力学的变分-伴随诠释，将量子可观测量定义为Fréchet灵敏度核，拓展了玻恩概率密度的范畴，建立了与时间对称诠释的联系，有望应用于量子控制与计量学。
中文摘要 AI 辅助
我们提出了量子力学的变分-伴随诠释，其中前向波函数与伴随波函数之间的相互作用定义了系统的广义灵敏度核。该Fréchet相互作用密度量化了波函数（或系统参数）的扰动对选定可观测量的影响。当伴随波函数取前向波函数的复共轭时，熟悉的玻恩概率密度作为特殊情况出现，此时相互作用密度为实数且非负。在该框架内，概率是由Fréchet相互作用密度描述的一种特殊正定形式的灵敏度。一般而言，变分-伴随诠释还会生成与其他量子可观测量相关的Fréchet灵敏度核，包括动量、能量和自旋。这表明玻恩概率密度属于与量子可观测量相关的更广泛的Fréchet灵敏度核类别。所提出的诠释还建立了与量子力学时间对称诠释的联系，并在量子控制和量子计量学中具有潜在的未来应用。
英文摘要
We present a variational--adjoint interpretation of quantum mechanics in which the interaction between forward and adjoint wavefunctions defines a general sensitivity kernel of the system. This Fréchet interaction density quantifies how perturbations in the wavefunction (or system parameters) influence a chosen observable. The familiar Born probability density appears as a special case when the adjoint wavefunction is chosen as the complex conjugate of the forward wavefunction, for which the interaction density becomes real and non-negative. Within this framework, probability is a particular positive-definite form of sensitivity described by the Fréchet interaction density. In general, the variational--adjoint interpretation also produces Fréchet sensitivity kernels associated with other quantum observables, including momentum, energy, and spin. This suggests that the Born probability density belongs to a broader class of Fréchet sensitivity kernels associated with quantum observables. The proposed interpretation also provides a connection with time-symmetric interpretations of quantum mechanics and possible future applications in quantum control and quantum metrology.
