Evolution of States of Quantum Systems of Finitely Many Particles

Abstract

Consider a system with a finite number N of identical particles with mass m interacting via a pair potential Φ, which depends only on the distance between particles. Denote by x ₁,…, x _N the vectors, which give the positions of particles in the 3-dimensional Euclidean space ℝ³, x _i =(x ¹ _i , x ² _i , x ³ _i , i = 1,2,…, N, where x ⁱ_α , α = 1,2,3, are the Cartesian coordinates of a vector x _i . The length of the vector x _i (the distance between the point x _i and the origin) is denoted by

$$ \left| {{x_i}} \right| = \sqrt {{{(x_i^1)}^2} + {{(x_i^2)}^2} + {{(x_i^3)}^2}} . $$