# WKB-approach for the 1D hydrogen atom

## 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.

## Key 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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Source: https://tomesphere.com/paper/1902.02189