# A question of phase density

1. Jul 23, 2008

### xylai

In the classical mechanics each system can be described by the phase density $$\rho(x,t)$$
, 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

$$\int\rho(x,t)^{2} dx$$ is constant in time.
But, as far as I know, due to the conservation of particles, $$\int\rho(x,t) dx$$
is constant in time.
I don’t know how he got the conclusion?

Last edited by a moderator: Apr 23, 2017