Polyelectronic wavefunctions

Hartree s method was to write a plausible approximate polyelectronic wavefunction (a guess ) for an atom as the product of one-electron wavefunctions ... 

A determinant is the most convenient way to write down the permitted functional forms of a polyelectronic wavefunction that satisfies the antisymmetry principle. In general, tf we have N electrons in spin orbitals Xi> X2 Xn (where each spin orbital is the product of a spatial function and a spin fxmction) then an acceptable form of the wavefunction is ... 

In conclusion, the discussion, the results, and the accompanying references of fhis chapter have documented, explained, and justified a set of formalisms and methods that can be used for the ab initio computation of fime-independenf and fime-dependent polyelectronic wavefunctions and for fhe quanfifafive undersfanding of basic quantities connected to a variety of field-free and field-induced unstable states (resonances) in the continuous spectra of afoms and molecules. 

It is easy to write down the form of an antisymmetric wavefunction for a polyelectronic atom if we recognize that Eq. (5.13) can be written in the... 

Just as for polyelectronic atoms, the electronic wavefunction for a molecule must be antisymmetric the Pauli principle. Thus, electron spin correlation is accommodated by the definition of the wavefunction as a Slater determinant whose elements are the occupied molecular orbitals. 

We now turn to the general case. What is an appropriate functional form of the wavefunction for a polyelectronic system (not necessarily an atom) with N electrons that satisfies the antisymmetry principle First, we note that the following functional form of the wavefunction is inappropriate ... 

Given the normal formulation of QM in ferms of sfationary states, including the case of resonances in fhe confinuous specfrum (see the superposition wavefunction of Eq. (2)), and fhe corresponding expressions which are measured on the energy axis, the question arises as to how easy it is to prepare unstable states in polyelectronic atoms and molecules and to observe their time-dependence. The answer involves more than one components. The most frequently mentioned is to consider the magnitude of fhe lifefime (provided, of course, fhaf if is known) relative to the duration of fhe excitation process. Obviously, if fhe former is much longer than the latter, the concept of a decaying sfafe is valid. 

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