# Introduction to Mathematical Physics/N body problem in quantum mechanics/Introduction

In this chapter, ${\displaystyle N}$ body problems that quantum mechanics can treat are presented. In atoms, elements in interaction are the nucleus and the electrons. In molecules, several nuclei and electrons are in interaction. Cristals are characterized by a periodical arrangment of their atoms. In this chapter, only spectral properties of hamiltonians are presented. Thermodynamical properties of collections of atoms and molecules are presented at next chapter. From a mathematical point of view, this chapter is an application of the spectral method presented at section chapmethspec to study linear evolution problems.