三维量子Hamilton-Jacobi方程与微观态
The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates
摘要：
在定常情形下，对于任意的势，我们用相应的薛定谔方程的解来求解三维量子Hamilton-Jacobi方程。然后，在分离变量的情况下，通过要求共轭动量在约化作用量中使用的薛定谔方程的解的任何线性变换下不变，我们清楚地确定了在一维，二维和三维连续的积分常数。在每一种情况下，我们分析建立量子哈密顿-雅可比方程描述的微观状态没有检测到的薛定谔方程在真正的波函数的情况下。
英文摘要：
In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrodinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrodinger equation used in the reduced action, we clearly identify the integration constants successively in one, two and three dimensions. In each of these cases, we analytically establish that the quantum Hamilton-Jacobi equation describes microstates not detected by the Schrodinger equation in the real wave function case.
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