一维Schrdinger方程在Coulomb型势中的束缚态精确解

Exact bound state solutions for one-dimensional Schrdinger equation with Coulomb-type potentials

利用级数解法求出了一维Schr dinger方程在势 -Ze2 x中的束缚态波函数和能级 .结果发现 ,其能级与1 n2 (n =1 ,2 ,3,… )成正比 ,束缚态波函数在原点的值为零 .分析了上述结论与关于势 -Ze2 x的能级与 1 (n +12 ) 2 (n为整数 )成正比的结论不相同的原因 .

The wave functions and the energy levels of bound states for one dimensional Schrdinger equations with potentials -Ze 2/x are given solved by the series expansion method.It is shown that the energy levels are proportional to 1/n 2(n=1,2,3,...)and the value of wave function of bound state at the origin is zero.The reasons of differences between our conclusion and the conclusion that the energy levels for potential -Ze 2/x are proportional to 1/(n+12) 2 with n an integer are analyzed.