The quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced. By dealing with the interaction between an electric field and the magnetic quadrupole moment, it is shown that an analogue of the Coulomb potential can be generated and bound state solutions can be obtained. Besides, the influence of the Coulomb-type potential on the harmonic oscillator is investigated, where bound state solutions to both repulsive and attractive Coulomb-type potentials are achieved and the arising of a quantum effect characterized by the dependence of the harmonic oscillator frequency on the quantum numbers of the system is discussed.

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The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to a harmonic and a linear confining potentials is investigated. It is shown that the interaction between the magnetic quadrupole moment and an electric field gives rise to an analogue of the Coulomb potential and, by confining this atom to a harmonic and a linear confining potentials, a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system is obtained. In particular, it is shown that the possible values of the angular frequency associated with the ground state of the system are determined by a third-degree algebraic equation.

Based on the single particle approximation [Dmitriev et al., Phys. Rev. C 50, 2358 (1994) and C.-C. Chen, Phys. Rev. A 51, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.

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