【摘要】 对于s态的双曲正切势场下的Schrdinger的径向方程,则能精确求出能量本征值和对应的波函数的表达式.对于非零的l态,则不能精确求解双曲势场下的在Schrdinger的径向方程.本文针对不能精确求解非零的l态,从另一方面出发,能利用近似的方法得到能量本征值和对应的本征函数的表达式.应用类似的Pekeris近似方法,将含有角动量的一项在r0处展开,省略高阶项,原双曲正切势场Schrdinger的径向方程变化成为超几何方程.应用超几何级数方法,得到了能量本征值和对应的本征函数的表达式.最后进行数值的验算,取两组不同的数值来计算能量本征值,得出结果基本一致,数值结果表明此法是可靠和有效的.更多还原

【Abstract】 For zero values,the radial Schrdinger equation for hyperbolic potential is solved exactly.For non-zero l values,the hyperbolic potential can not be solved exactly.In this work,for non-zero l values,an approximation method has been applied in another way to obtain energy eigenvalues and corresponding wavefuctions.So similar Pekeris approximation method has been introduced,the angular momentum term is being approximate expanded nearby r0 and higher-order are neglected,radial Schrdinger equation is modified as a hypergeometric equation.The energy eigenvalues and corresponding wavefuctions has been obtained through the hypergeometric series method.Finally,the results which using the pair of data obtained here are shown to be in good agreement,the numerical of eigenvalues demonstrate reliable and effectiveness of the proposed method.更多还原