Electromagnetic generalized Lorenz-Mie Theory (GLMT) describes the interaction between an arbitrary shaped electromagnetic laser beam and a homogeneous sphere. with an isotropic and linear material. We are interested in the study of analogies and differences between the electromagnetic GLMT and a quantum GLMT and to their exploitation. To build a quantum GLMT, a prerequisite is the description of the incident quantum state in terms of spherical partial waves. In this framework, this paper deals with the expansions in free space of arbitrary quantum wave packets. quantum laser beams, and quantum Gaussian (on-axis and off-axis) laser beams in terms of free spherical waves.