The aim of this work is to develop exact methods for crystal potentials and wave functions, which would allow to calculate the energy spectra of the electron states in various solids without fitting and use of corrective factors. The article considers the number of structural units of clusters and their physical properties of the GaAs structure. The resulting cluster is investigated and studied based on computer simulation as. We introduced an additional concept of interspheral space, shows certain characteristics that are present in the real space of the crystal lattice in the formation of the structure. Values describing the interspheral space are directly involved in describing the properties of direct and reciprocal space. The values of the variables describe the quasi-bound states of the structural units of the direct and reciprocal spaces. Quasi-bound states determine quantities that are parameters of the characteristics of the corresponding spaces. Computer modeling determines the spatial coordinates relative to the selected number of structural elements of the cluster in direct space. Solving the Poisson equation in reciprocal space, we obtain the electron density and the allowed values of the energy levels. An approach is discussed using the proposed concept of the intersphere space to the structure of GaAs clusters and the results of a computer-analytical study based on this concept, satisfying the solution of the equation of the intersphere oscillator.