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对于一般形式的含时线性势, 通过假设波函数形式的方法得到了Schr?dinger方程的精确和完备解. 同时指出, 用两个波函数φ(t)〉和ψ(t)〉定义的坐标和动量的矩阵元〈φ(t)xψ(t)〉和〈φ(t)pψ(t)〉满足经典形式的运动方程. 按照量子力学的系综理论, 这样的经典形式的运动方程实际上是流体方程. 进一步研究发现, 对于任意形式的线性系统有类似的结论.
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关键词:
- 线性势 /
- Schr?dinger方程 /
- Heisenberg对应原理 /
- 经典运动方程
For the general time-dependent linear potential, the exact and complete solution of the Schr?dinger equation was obtained by assuming a form of wave function. Meanwhile, it was pointed out that the matrices φ(t)〉和ψ(t)〉 defined by the two wave functions 〈φ(t)xψ(t)〉和〈φ(t)pψ(t)〉 satisfy classical equations of motion. According to the ensemble theory of quantum mechanics, such classical equations describe the motion of fluid. A further research shows that similar conclusions apply to any linear system.-
Keywords:
- linear potential /
- Schr?dinger equation /
- Heisenberg correspondence principle /
- classical equation of motion
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