The bound states for the symmetric shifted Coulomb potential
- 1 October 1978
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 19 (10) , 2165-2170
- https://doi.org/10.1063/1.523573
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 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.Keywords
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