Canonical ensemble: Difference between revisions

Revision as of 12:02, 18 February 2008

Variables:

The classical partition function for a one-component system in a three-dimensional space, $Q_{N V T}$ , is given by:

Q_{N V T} = \frac{V^{N}}{N! Λ^{3 N}} \int d (R^{*})^{3 N} \exp [- β U (V, (R^{*})^{3 N})]

where:

$β : = \frac{1}{k_{B} T}$ , with $k_{B}$ being the Boltzmann constant, and T the temperature.

$U$ is the potential energy, which depends on the coordinates of the particles (and on the interaction model)

${(R^{*})}^{3 N}$ represent the 3N position coordinates of the particles (reduced with the system size): i.e. $\int d (R^{*})^{3 N} = 1$

@@ Line 5: / Line 5: @@
 * Volume, <math> V </math>
-* Temperature, <math> T </math>
+* [[Temperature]], <math> T </math>
 == Partition Function ==
@@ Line 18: / Line 18: @@
 * <math> \Lambda </math> is the [[de Broglie thermal wavelength]] (depends on the temperature)
-* <math> \beta = \frac{1}{k_B T} </math>, with <math> k_B </math> being the [[Boltzmann constant]], and ''T'' the [[temperature]].
+* <math> \beta := \frac{1}{k_B T} </math>, with <math> k_B </math> being the [[Boltzmann constant]], and ''T'' the [[temperature]].
 * <math> U </math> is the potential energy, which depends on the coordinates of the particles (and on the interaction model)