结构化学波函数向量概念难点的数学解释

An Interpretation on Wave Function in Structural Chemistry Course

结构化学课程中一般把波函数看作向量,把两波函数乘积的积分看作向量的内积。这一概念理解起来较困难。为此,笔者建议把积分区域划分成体积元的拼接,并把每个体积元定义为向量的一个维度。因此,向量的维度等于积分区域体积元的数量。把函数在各体积元内的平均值看作向量在这个维度的取值。把体积元的体积看成两个常数因子的乘积,再把这两个常数因子归并到函数取值中。这样,积分就转变成了两向量的点积。

In Quantum Chemistry,the wave function is regarded as vector,and the integral between two functions is regarded as the dot product between two vectors.However,this viewpoint is very hard to accept.A new idea was proposed in order to facilitate the understanding of the viewpoint.In the method,the definition domain of the integrand was divided as many volume elements,and each volume element corresponded to a dimension of vector.So that the dimension of the vector was equals to the number of volume elements that the domain contained.The value of vector component at a volume element can be represented by the mean value of the corresponding function within the volume element.The volume of a volume element was regarded as the product of two constants,and the two constants can be regarded as the coefficient of the two function values within the volume element,respectively.Then the integral of function became the dot product of two vectors naturally.