# A semiclassical treatment of the interaction of non-uniform electric fields with the electric quadrupole moment of a neutral particle

## TL;DR

This paper uses the WKB approximation to analyze how a neutral particle's electric quadrupole interacts with non-uniform electric fields, revealing conditions for discrete energy spectra in specific cases.

## Contribution

It introduces a semiclassical approach to study quadrupole interactions with non-uniform fields, providing new insights into energy quantization for neutral particles.

## Key findings

- Discrete energy spectra can be achieved for s-waves in certain field configurations.
- The WKB approximation effectively models quadrupole-field interactions.
- Specific cases demonstrate quantized energy levels in non-uniform electric fields.

## Abstract

By applying the WKB (Wentzel, Kramers, Brillouin) approximation, we analyse the interaction of the electric quadrupole moment of a neutral particle with radial electric fields produced by a non-uniform electric charge densities. Then, we show particular cases of this interaction where a discrete spectrum of energy can be achieved for the s-waves of the neutral particle.