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On the finiteness of the discrete spectrum of the energy operator of negative atomic and molecular ions

G. M. Zhislin


Abstract: Let $H$ be the energy operator of an atom with $n$ electrons in which allowance is made for the motion of the nucleus or the energy operator of $n$ electrons in the field of $n_0$ fixed nuclei. It is shown that in the space of functions defined by an arbitrary irreducible representation of the symmetry group of $H$ the number of discrete eigenvalues of $H$ cannot be infinite if the total charge of the system is less than –1 (in atomic units). Previously, a similar result was known only for $n=2$.

UDC: `

Received: 20.08.1970

 English version: Theoretical and Mathematical Physics, 1971, 7:3, 571–578

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