概率流与轨迹表示
Probability Current and Trajectory Representation
摘要：
在稳态情况下，给出了实和复波函数的统一形式，导出了三维空间中的量子Hamilton-Jacobi方程。克服了玻姆理论中出现的诸如在实波函数情况下共轭动量为零等困难。在一维空间中，提出了量子Hamilton-Jacobi方程的一种新的通解形式，它直接导出了薛定谔波函数的一般形式。对于非束缚态，证明了在复空间中波函数的伸缩加旋转下的约化作用量的不变性意味着微观态不出现。对于束缚态，它表明，一些自由的存在，并引起的表现形式的微观状态没有检测到的薛定谔波函数。
英文摘要：
A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing value of the conjugate momentum in the real wave function case are surmounted. In one dimension, a new form of the general solution of the quantum Hamilton-Jacobi equation leading straightforwardly to the general form of the Schrödinger wave function is proposed. For unbound states, it is shown that the invariance of the reduced action under a dilatation plus a rotation of the wave function in the complex space implies that microstates do not appear. For bound states, it is shown that some freedom subsists and gives rise to the manifestation of microstates not detected by the Schrödinger wave function.
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