# Quantum effects on an atom with a magnetic quadrupole moment in a region with a time-dependent magnetic field

## TL;DR

This paper analyzes how a time-dependent magnetic field influences an atom with a magnetic quadrupole moment, revealing induced electric fields, Landau-type quantization, and exact solvability of the Schrödinger equation.

## Contribution

It demonstrates that the magnetic quadrupole moment interacts with time-dependent magnetic fields to produce Landau-type quantization and derives an exact Schrödinger equation for this system.

## Key findings

- Time-dependent magnetic fields induce electric fields affecting the atom.
- Landau-type quantization arises due to the magnetic quadrupole interaction.
- The Schrödinger equation for the system can be solved exactly.

## Abstract

The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schr\"odinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schr\"odinger equation can be solved exactly. It is also analysed this system subject to scalar potentials.