标题： 一维波函数的量子哈密顿-雅可比方程的数值解和类似WKB的表示形式 显示英文标题

标题： Numerical solutions of the quantum Hamilton-Jacobi equation and WKB like representations for one dimensional wave functions

摘要： 通过量子哈密顿-雅可比方程的数值解，得到了一维波函数的一般WKB类似表示。 该表示在经典禁止区域中是唯一的，而在允许区域中，每个波函数对应于QHJE的一族解。 该方法已应用于各种系统，具有不同的能量和初始条件。 在所有研究的情况下，所获得的波函数准确地再现了通过其他方式解析或数值计算的薛定谔方程的解。 给出了一些关于简谐振子和径向库仑运动的结果。 显示英文摘要

摘要： By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the allowed one, each wave function corresponds to a one parameter family of solutions of the QHJE. The method has been applied to various systems, with different energies and initial conditions. In all investigated cases, the wave functions so obtained accurately reproduce the solutions of the Schr\"odinger equation, analytically or numerically computed by other ways. Some results for harmonic oscillator and radial Coulomb motion are presented.