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1、量子力学例题第二章 一．求解一位定态薛定谔方程1．试求在不对称势井中的粒子能级和波函数[解]薛定谔方程: 当 , 故有 利用波函数在 处的连续条件由 处连续条件: 由 处连续条件: setup,graspingpartybuildingworkinnon-publiceconomicandso
2、cialorganizations,expandingthecoverageofthepartybuilding.Conscientiouslyimplementthepartymembersthewholepublicity,votingandmobilepartymembersmanagementsystem,strengthenandimproveparty 给定一个n值,可解一个, 为分离能级.2． 粒子在一维势井中的运动 求粒子的束缚定态能级与相应的归一化定态波函数[解]体系的定态薛定谔方程为当
3、时对束缚态 解为 在 处连续性要求将 代入得 setup,graspingpartybuildingworkinnon-publiceconomicandsocialorganizations,expandingthecoverageofthepartybuilding.Conscientiouslyimplementthepartymembersthewholepublicity,votingandmobilepartymembersmanagementsystem,strengthenandimprov
4、eparty又 相应归一化波函数为: 归一化波函数为:3 分子间的范得瓦耳斯力所产生的势能可近似地表示为 求束缚态的能级所满足的方程[解]束缚态下粒子能量的取值范围为 setup,graspingpartybuildingworkinnon-publiceconomicandsocialorganizations,expandingthecoverageofthepartybuilding.Conscientiouslyimplementthepartymembersthewhole
5、publicity,votingandmobilepartymembersmanagementsystem,strengthenandimproveparty当 时 当 时 薛定谔方程为令 解为 当 时 令 解为当 时 薛定谔方程为setup,graspingpartybuildingworkinnon-publiceconomicandsocialorganizations,expandingthecoverageofthepartybuilding.Cons
6、cientiouslyimplementthepartymembersthewholepublicity,votingandmobilepartymembersmanagementsystem,strengthenandimproveparty 令 薛定谔方程为解为由 波函数满足的连续性要求,有 setup,graspingpartybuildingworkinnon-publicecon
7、omicandsocialorganizations,expandingthecoverageofthepartybuilding.Conscientiouslyimplementthepartymembersthewholepublicity,votingandmobilepartymembersmanagementsystem,strengthenandimproveparty 要使 有非零解 不能同时为零 则其系数组成的行列式必须为零 计算行列式,得方程例题主要类
8、型:1.算符运算; 2.力学量的平均值; 3.力学量几率分布.一. 有关算符的运算1.证明如下对易关系(1) (2) (3) (4) setup,graspingpartybuildingworkinnon-publiceconomicandsocialorganizations,expandi
