In the classical mechanics each system can be described by the phase density [tex]\rho(x,t)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

, which is evolved by Liouville's equation.

Recently I read a paper: http://www.sciencedirect.com/scienc...6104324&md5=d41e737ddc2514dbbeca4a99047e66f7"(Y, Gu, PLA, 149, 95 (1990)). In it, it says that

[tex]\int\rho(x,t)^{2} dx [/tex] is constant in time.

But, as far as I know, due to the conservation of particles, [tex]\int\rho(x,t) dx [/tex]

is constant in time.

I don’t know how he got the conclusion?

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# A question of phase density

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