量子力学中的相空间轨道
Phase space trajectories in quantum mechanics
摘要：
量子力学的一种改进的表示法使人们对量子态和经典态之间的关系有了新的认识。在这种方法中，量子态空间分裂为经典力学的状态空间和希尔伯特空间的乘积，而观测值的期望值分解为它们的经典值加上量子修正。在一定的假设下，薛定谔方程的时间演化会保持分裂，而量子态经典部分的时间演化则受汉密尔顿方程的支配。新的表示是从通常的希尔伯特空间表示的量子力学通过引入一个规范自由度的含时么正变换，其次是一个非传统的规范固定条件。
英文摘要：
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.
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