Page 232 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

ELECTRONIC CHARGE DENSITY OF QUANTUM SYSTEMS 215

where we have set
Thus the integration in the time variable involved in eq. (B.1) yields

where we have utilized the definition of the Airy function [33]

From the latter result, eq. (B.1) is finally cast into the form

Appendix C
Eq. (2.14) in the text can be derived in a straightforward way after choosing the z-axis
along the direction of the vector , so that . Then , eq. (2.13), can
be written down in the form

By a simple variable change the integration in is expressible in terms of the Airy
function of proper argument [see eq. (B.3)], so that