量子粒子的欧拉和牛顿动力学
Eulerian and Newtonian dynamics of quantum particles
摘要：
我们推导出流体力学类型的经典方程（欧拉方程和连续性方程），薛定谔方程作为极限情况。结果表明，对应于量子系统的统计系综，由薛定谔方程描述，可以看作是服从理想气体定律的无粘气体，具有快速振荡的温度变号。该统计系综执行由平滑平均运动和快速振荡组成的复杂运动。结果表明，统计系综的平均运动可用薛定谔方程描述。提出了一个与所考虑的流体力学系统相对应的经典力学范围内的量子运动模型。
英文摘要：
We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and described by the Schrodinger equation, can be considered as an inviscid gas obeying the ideal gas law with quickly oscillating sign-alternating temperature. This statistical ensemble performs the complex movements consisting of smooth average movement and fast oscillations. It is shown that average movements of statistical ensemble are described by Schrodinger equation. A model of quantum motion within the limits of classical mechanics which corresponds to the considered hydrodynamic system is suggested.
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