Evolution of States of Quantum Systems of Finitely Many Particles

  • D. Ya. Petrina
Part of the Mathematical Physics Studies book series (MPST, volume 17)


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 i 1 , x i 2 , x i 3 , i = 1,2,…, N, where x α i , 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
$$ \left| {{x_i}} \right| = \sqrt {{{(x_i^1)}^2} + {{(x_i^2)}^2} + {{(x_i^3)}^2}} . $$


Density Matrix Quantum System Commutation Relation Selfadjoint Operator SchrOdinger Equation 
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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • D. Ya. Petrina
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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