The generalized Sturmian secular equations

The generalized Sturmian secular equation (23) has several remarkable features ... 

Thus, when Goscinskian configurations are used, the generalized Sturmian secular equation for atoms (23) takes on the form ... 

Since only Coulomb potentials are involved, the matrix T v, v turns out to be energy independent. Its elements are pure numbers that depend only on N, the number of electrons, and are independent of the nuclear charge Z. The roots lK of the energy-independent interelectron repulsion matrix T v, v are also pure numbers (Table 1). In the large-Z approximation, the generalized Sturmian secular equation (41) reduces to the requirement ... 

To obtain the generalized Sturmian secular equations, we substitute the superposition (6) into the many-particle Schrodinger equation (5) ... 

In the present paper, generalized Sturmians are introduced in Section 2. Their potential-weighted orthonormality relations (Section 3) permit us to write down a peculiar secular equation (Section 4). Examples of its solution for atomic problems are given in Section 5. In these calculations, generalized... 

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