When I was reading statistical Mechanics it has written "by using phase space , the 6N(3N coordinate axes and 3N momentum axes) coordinates can represent the position and momentum of all the molecules at a given time". But according to Heisenberg Uncertainty principle it is not possible. Can anyone help me in this?

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    $\begingroup$ Whatever you are reading is considering classical particles. They will almost certainly get to considering quantum mechanics, but there are other complications which mean that classical particles are the simplest place to start. $\endgroup$ – By Symmetry Mar 7 '18 at 14:16
  • $\begingroup$ Please edit your subject line to be more specific. People will not read questions if they have no idea whether or not they can contribute an answer. $\endgroup$ – garyp Mar 7 '18 at 15:29
  • $\begingroup$ Ok I will do it $\endgroup$ – user156273 Mar 7 '18 at 15:51

In classical Statistical Mechanics a statistical ensemble is described by a distribution of points in phase space consisting of the 6N generalized coordinates and momenta. As you correctly observe, in quantum mechanics, you cannot specify exact values for canonically conjugate variables and thus cannot use points in phase space. Therefore you need to describe your system in the framework of Quantum Statistical Mechanics where a statistical ensemble is described by a density operator.


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