# A doubly anharmonic oscillator in an induced electric dipole system

## TL;DR

This paper investigates the quantum behavior of an induced electric dipole atom in combined magnetic and electric fields, revealing analytical solutions and quantum effects dependent on magnetic field quantization.

## Contribution

It introduces a novel analogue of a doubly anharmonic oscillator in an induced electric dipole system and derives analytical solutions to the Schrödinger equation.

## Key findings

- Analytical solutions to the Schrödinger equation were obtained.
- Quantum effects depend on discrete magnetic field values.
- The system behaves as a spinless particle in an anharmonic potential.

## Abstract

The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schr\"odinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.