The problem of nonrelativistic one-dimensional particle motion in а Coulomb attractive field which has been under investigation for а long time is subjected to examination. On the basis of the physical principles that the energy levels are independent of the choice of length scales, that there is no Clauder effect, and tbat there are no bound states in the repulsive field, а self-consistent expansion of the Hamiltonian of а one-dimensional hydrogen atom with uniquely de fined parity-nondegenerate levels and а stable ground state is found. New expressions are found for the even wave functions.
Departrnent of Theoretical Physics
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