Exact solutions of the one-dimension Coulomb potential: A case of non hermiticity with a real spectrum

Gilles Abramovici

Université Paris, Laboratoire de Physique des Solides, Orsay, France

I would like to present and discuss the exact solutions of the 1d-Coulomb potential 1/|x| in Schrödinger equation, which revealed non-hermitian in the attractive case. The eigenvalues are still real and the bound state spectrum is divided into two compounds : standard Rydberg solutions with Rydberg energies Ei/n2 ; anomalous solutions with energies Ei/(n+1/2)2.

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