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ELECTRONIC CHARGE DENSITY OF QUANTUM SYSTEMS 207
with
A series of manipulations [see Appendix B, eq. (B.4)] allows the function to be
expressed as follows
where we have set
and Ai[x] denotes the Airy function of argument x [33].
The replacement of the result for eq. (2.10), into eq. (2.8) yields for the
electronicdensity
where
The expression for can be elaborated rather simply, [see Appendix C, eq. (C.4)]
Indefinite integrals involving products of Airy functions and/or their derivatives can be
evaluated without many difficulties [34]. Thus,
