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--- basic_tools:phase_space [2018/11/13 22:27]
supeng_hong [Intuitive]
+++ basic_tools:phase_space [2020/04/03 10:50]
81.217.94.109 small fixes
@@ Line 17: / Line 17: @@
 Try to imagine a
 'space' of a large number of dimensions, one dimension for each of the
-coordinates $x_1, x_2,\ldots$, $p_1, p_2,\ldots$ (Mathematical spaces often have many;
+coordinates $x_1, x_2,\ldots$, $p_1, p_2,\ldots$ (Mathematical spaces often have many
 more than three dimensions.) This space is called phase space (see Fig. 5.10).
-For n unconstrained particles, this be a space of 6n dimensions (three,
+For n unconstrained particles, this is a space of 6n dimensions (three
 position coordinates and three momentum coordinates for each particle). The
 reader may well worry that even for a single particle this is already twice as
 many dimensions as she or he would normally be used to visualizing! The
 secret is not to be put off by this. Whereas six dimensions are, indeed, more
-dimensions than can be readily pictured, it would actually not be of much
+dimensions than can be readily pictured, it would actually not be of much use
-to us if we were in fact able to picture it. For just a room full of
+to us if we were in fact able to imagine it. For just a room full of
 molecules, the number of phase-space dimensions might be something like