在量子力学中，波函数必须具备单值、连续和有限性这三个标准化条件，对于波函数加上这样的条件后就会自然的给出能量量子化.对于无穷级数收敛和发散的判定在量子力学中具有非常重要的意义.现行的教科书基本上都是采用同级级数发散来说明该级数也发散.本文在发散级数的比较方面，采用了一个更容易使学生理解的方法，那就先找出一个比该级数小的发散级数，然后证明小级数发散，再由此说明大的级数一定发散，这样讲解不仅使学生能够很快接受，更重要的是在逻辑上 　　更完备.

In quantum mechanics，the wave function must obey the three standard conditions，such as single value，continuous and finite，which give naturally energy quantization after the wave function under such conditions.The determination of convergence and divergence of infinite series is very important in quantum mechanics. The current textbooks use basically the same grade diverging to show that the series diverges.In comparison with divergent series，we adopt a more easy method to make students understand，find a better rather than the first series of small divergent series，and then prove little diverges，to illustrate that the series of great divergence.This interpretation not only enables students to accept quickly，more important is logically more complete.