Title: The bound states for the symmetric shifted Coulomb potential
Abstract:We investigate the bound states for the symmetric one-dimensional shifted Coulomb potential, V (x) =−2s (‖x‖ +d)−1. Explicit approximate expressions for the infinite number of bound-state energies are...We investigate the bound states for the symmetric one-dimensional shifted Coulomb potential, V (x) =−2s (‖x‖ +d)−1. Explicit approximate expressions for the infinite number of bound-state energies are obtained. For small s, the ground-state energy is O (s2 ln2sd), whereas the energies of the excited states are O (s2). We prove that the square roots of the binding energies form approximately a harmonic progression both for the even solutions and for the odd solutions. This is also true for the sequence of all solutions when sd is not small. However, when sd≪1, this sequence shows an interesting odd–even staggering phenomenon.Read More
Publication Year: 1978
Publication Date: 1978-10-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 9
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