Calculating ∫∞−∞e−ax2eibxdx

manpreet Best Answer 2 years ago

In my syllabus about quantum mechanics, they state that the following integral can be easily calculated:

if it is known that

This isn't indeed that hard, if aa is real. But they use it in a derivation, where aa has an imaginary part. I hope someone can show me, how this is also valid when aa and bb are complex. (If needed you may assume that it is known that the integral is valid for