The Analytical Model of a Polyatomic Crystal Lattice With a Continuous Potential

Due to development of artificial intelligence systems, nanotechnology and quantum systems for signal transmission and information processing, detailed description and modeling physical process at the quantum level is very relevant for today. The accurate analytical model (Croning-Penny model) for a crystal lattice with stepwise change in potential has been developed and analyzed in scientific literature in detail. In well-known papers a structure with double-cell period only has been under consideration. However cases of continuous potential have been studied by using numerical and semi-analytical methods only. The authors propose the accurate analytical model for the case of continuous potential. The fundamental matrix of Schrodinger equation is obtained by using the Floquet theory, fundamental matrix of an interval with constant parameters and continuous conditions for wave function and it's derivation. The analysis of the obtained solution gives us bandgap structure of polyatomic crystal lattices. The numerical calculations proving correctness of the obtained results are present too.