Popa Alexandru
Laser Department, Institute of Atomic Physics, National Institute for Laser, Plasma and Radiation Physics, Bucharest, Magurele, Romania.
J Chem Phys. 2005 Jun 22;122(24):244701. doi: 10.1063/1.1943387.
In the hidden variable theory, Bohm proved a connection between the Schrodinger and Hamilton-Jacobi equations and showed the existence of classical paths, for which the generalized Bohr quantization condition is valid. In this paper we prove similar properties, starting from the equivalence between the Schrodinger and wave equations in the case of the conservative bound systems. Our approach is based on the equations and postulates of quantum mechanics without using any additional postulate. Like in the hidden variable theory, the above properties are proven without using the approximation of geometrical optics or the semiclassical approximation. Since the classical paths have only a mathematical significance in our analysis, our approach is consistent with the postulates of quantum mechanics.
在隐变量理论中，玻姆证明了薛定谔方程与哈密顿 - 雅可比方程之间的联系，并表明存在经典路径，对于这些经典路径广义玻尔量子化条件是有效的。在本文中，我们从保守束缚系统情况下薛定谔方程与波动方程的等价性出发，证明了类似的性质。我们的方法基于量子力学的方程和假设，不使用任何额外的假设。与隐变量理论一样，上述性质的证明不使用几何光学近似或半经典近似。由于经典路径在我们的分析中仅具有数学意义，所以我们的方法与量子力学的假设是一致的。
