First of all, we should know a conclusion: ∫ [-∞→ +∞] e (-x? )dx = √ π。 For the specific calculation method, please refer to an example in the polar coordinate part of double integral in the second volume of advanced mathematics textbook of Tongji University ∫ e (ix? )dx

=e^(-i)∫e^i*e^(ix？ )dx

=e^(-i)∫e^(-x？ )dx

=√πe^(-i)

=√π(cos 1-isin 1

Then write (p'-p), not counting, just write this answer. Remember to add the previous (1/ root number 2π times h) to form the whole function, otherwise it is wrong. (1/ root number 2π times h) is used to calculate angular momentum, and you can write the answer directly by adding the corresponding function in front.

Extended data

For example:

Calculate the integral of ∫ (x 2) exp (-x 2) dx:

f(x)=[ 1/√(2pi)]*exp(-x^2)

EX=0DX= 1

Ex 2 = dx+(ex) 2 =1= ∫ x2f (x) dx from negative infinity to positive infinity.

therefore

∫x^2*[ 1/√(2pi)]*exp(-x^2)dx= 1

∫(x^2)exp(-x^2)dx=√(2pi)