To study the scattering of electromagnetic radiation by a spherical metallic nanoparticle with quantum spatial dispersion, we develop the standard nonlocal Mie theory by allowing for the excitation of the quantum longitudinal plasmon modes. To describe the quantum nonlocaleffects, we use the quantum longitudinal dielectric function of the system. As in the standard Mietheory, the electromagnetic fields are expanded in terms of spherical vector wavefunctions. Then, the usual Maxwell boundary conditions are imposed plus the appropriate additionalboundary conditions. Examples of calculated extinction spectra are presented, and it is found that the frequencies of the subsidiary peaks, due to quantum bulk plasmon excitations exhibit strong dependence on the quantum spatial dispersion.
