On the use of multipole expansion of the Coulomb Potential in quantum chemistryстатья
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Аннотация:Some features of the multipole expansion of the Coulomb potential V for a system of point charges are studied. It is shown that multipole expansion is convergent both locally in L2(R3) and weakly on some classes of functions. One-particle Hamiltonians Hn = H0 + Vn, where H0 is the kinetic energy operator and Vn is the n-th partial sum of the multipole expansion of V, are discussed, and the convergence of their eigenvalues to those of H = H0 + V with increasing n is proved. It is also shown that the discrete spectrum eigenfunctions of Hn converge to those of H both in L2(R3) (together with their first and second derivatives) and uniformly on R3.