关于有心力场束缚定态的一个关系式

A relationship about the stationary bound state of centrally symmetric potential

当一个微观粒子在有心力场中运动并处于束缚定态时,它所受力的期望值有一个重要关系式.本文对此关系式从不同角度给出了几种不同的证明,讨论了其物理意义.特别还讨论了该关系式的成立条件,澄清了若干文献关于该式叙述或者理解的不确切之处.

For a microscopic particle in a centrally symmetric potential and in its stationary bound state, there is a relationship about the expectation value of the force to the particle. In this paper, several different proofs to this relationship are presented with a discussion to its physics connotation. In addition, the conditions necessary for the relationship to hold is discussed, hence the related misunderstanding or inaccuracy currently in literature is clarified.