  Analogous to Landau quantization related to a neutral particle possessing an
electric quadrupole moment, we generalize such Landau quantization to include
position-dependent mass (PDM) neutral particles. Using cylindrical coordinates,
the exact solvability of PDM neutral particles with an electric quadrupole
moment moving in electromagnetic fields is reported. The interaction between
the electric quadrupole moment of a PDM neutral particle and a magnetic field
in the absence of an electric field is analyzed for two different radial
cylindrical PDM settings. Next, two particular cases of radial electric fields
(E={\lambda}\r{ho}/\r{ho} and E={\lambda}\r{ho}/2\r{ho}) are considered to
investigate their influence on the Landau quantization (of this system using
the same models of PDM settings). The exact eigenvalues and eigenfunctions for
each case are analytically obtained.
