论文标题
量子力学中的相空间轨迹
Phase space trajectories in quantum mechanics
论文作者
论文摘要
量子力学的改编表示，阐明了量子状态与经典状态之间关系的新启示。在这种方法中，量子状态的空间分为经典力学和希尔伯特空间的状态空间的产物，并且可观察物的期望值分解为其经典价值以及量子校正。在某些假设下，在schrödinger方程的时间演变下保留了分裂，量子状态的经典部分的时间演变受汉密尔顿方程的控制。新的表示是通过在时间依赖性的统一转换中引入量规自由度的通常的量子力学的希尔伯特空间表示，然后是非惯性规格固定条件。
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and a Hilbert space, and expectation values of observables decompose into their classical value plus a quantum correction. The splitting is preserved under time evolution of the Schrödinger equation under certain assumptions, and the time evolution of the classical part of a quantum state is governed by Hamilton's equation. The new representation is obtained from the usual Hilbert space representation of quantum mechanics by introducing a gauge degree of freedom in a time-dependent unitary transformation, followed by a non-conventional gauge fixing condition.
