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Evolution of States of Quantum Systems of Finitely Many Particles

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

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

Keywords

Density Matrix Quantum System Commutation Relation Selfadjoint Operator SchrOdinger Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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