WKB-approach for the 1D hydrogen atom
A.M. Ishkhanyan, V.P. Krainov
TL;DR
This paper uses the WKB approximation to derive exact energy levels and wave functions for the one-dimensional hydrogen atom, providing a detailed analytical approach to its quantum states.
Contribution
It introduces a method to obtain exact solutions for the 1D hydrogen atom using WKB approximation, which is novel for this potential.
Findings
Exact quantum energies derived for even and odd states.
Wave functions explicitly calculated for the 1D Coulomb potential.
Demonstrates the effectiveness of WKB in solving 1D quantum systems.
Abstract
Taking into account results of WKB-approximation, we derive exact quantum energies and wave functions of even and odd states in the one-dimensional Coulomb potential
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