In this work, we propose a model for achieving the Landau quantization for an electric quadrupole moment. We consider the electric charge and the electric dipole moment of an electric charge distribution to vanish and build a model for the Landau quantization for an electric quadrupole moment.

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In this paper, we use Hermitian linear invariants and the Lewis and Riesenfeld invariant method to obtain the general solution of the Schrödinger equation for a mesoscopic RLC circuit with time-dependent resistance, inductance, capacitance and a power source and represent it in terms of an arbitrary weight function. In addition, we construct Gaussian wave packet solutions for this electromagnetic oscillation circuit and employ them to calculate the quantum fluctuations of the charge and the magnetic flux as well as the associated uncertainty product. We also show that the width of the Gaussian packet and the fluctuations do not depend on the external power.

Basing on the analogue Landau levels for a neutral particle possessing an induced electric dipole moment, we show that displaced states can be built in the presence of electric and magnetic fields. Besides, the Berry phase associated with these displaced quantum states is obtained by performing an adiabatic cyclic evolution in series of paths in parameter space.

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