标题： 关于波函数节点和量子哈密顿-雅可比解 显示英文标题

标题： On the nodes of wave function and the quantum Hamilton-Jacobi solution

摘要： 我们给出定态量子哈密顿-雅可比方程的解析解。 了解里卡蒂方程与量子哈密顿-雅可比方程之间的强关系，我们开发了一种简单的方法来获得精确解。 然后，为了证明所提出方法的有效性，我们使用了两种中心势：三维谐振子和库仑势，两者都有束缚态。 最后，我们计算了完全量子版本中的作用量-角度变量，以实现与波函数节点的连接。 显示英文摘要

摘要： We present the analytic solution for the stationary quantum HamiltonJacobi equation. Knowing the strong relation between the Riccati and quantum Hamilton-Jacobi equations, we develop a simple method to obtain the exact solution. Then, in order to prove the validity of the proposed method, we use two central potentials: the three-dimensional harmonic oscillator and Coulomb potential, both with bound-states. Finally, we compute the action-angle variables in a entirely quantum version for to achieve connect with the nodes of the wave function.