Page 231 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

214 G. P. ARRIGHINI AND C. GUIDOTTI

and therefore

Taking into account that operators associated with different labels j commute between
each other, form eqs. (A.1), (A.3), (A.6) we get

The diagonal matrix element of the QMP can therefore be written in the form

The evaluation of the simple integral contained in eq. (A.8) would lead, of course, to the
known expression for the QMP of the system under study [32].

Appendix B

The function of eq. (2.9) is conveniently expressed as follows

with

The Fourier representation of the Dirac delta function leads then to the result

and therefore,

The cubic form in t appearing in the exponential of eq. (B.1) is expressible as