量子力学矩阵元的经典极限

CLASSICAL LIMIT OF QUANTUM MECHANICAL MATRIX ELEMENTS

本文研究了量子力学矩阵元的经典极限，用新的方法证明了如下定理：在分立谱情况下，量子力学矩阵元ｆｎｍ的经典极限是相应经典力学量ｆ（ｔ）之Ｆｏｕｒｉｅｒ级数展开的第ｎ－ｍ个分量；在连续谱情况下，量子力学矩阵元ｆＥ＇Ｅ，Ｅ与Ｐｌａｎｃｋ常量的乘积ｆＥ＇Ｅ的经典极限是相应经典力学量ｆ（ｔ）之Ｆｏｕｒｉｅｒ积分展开的第ω次分量。

The classical limit of quantum mechanical matrix elements is studied.A new method is introduced to prove the following theorem:For a system of discrete spectrum,the matrix elements fnmin classical limit become the(n-m)th components of its Fourier series;for a system of continuous spectrum,the matrix elements fE'E become the ωth components of its Fourier integral.