Page "Wave packet" Paragraph 83

The factor involving ε is an infinitesimal quantity which is there to make sure that integrals over K are well defined.

In the limit that ε → 0, K becomes purely oscillatory, and integrals of K are not absolutely convergent.

In the remainder of this section, it will be set to zero, but in order for all the integrations over intermediate states to be well defined, the limit ε → 0 is to be only taken after the final state is calculated.