一些定态波函数的经典极限

The Classical Limit of some Stationary State wave Functions

摘要: 研究了一维谐振子的波函数和氢原子波函数的经典极限,首先定义了一种特殊的单粒子系综,即均匀系综,其次明确了经典极限是一种综合极限,即量子数n→∞,普朗克常数h→0但保持能量E(n,h)为某一固定值的极限,这种极限实质是大量子数极限但可使能量变化取无限小量。引入均匀系综定义并用综合极限方法,严格证明了一维谐振子的定态波函数和氢原子的定态波函数的精典极限都是某种均匀系综。

Abstract: The classical limits of the one dimensional harmonic oscillator wave function and the hydrogen wave function are studied in this paper. It is proved that these classical limits,described classically,are for a single particle ensemble,not a single particle.