Editing Canonical ensemble

Variables: 

* Number of Particles, <math> N </math>

* Volume, <math> V </math>

* Temperature, <math> T </math>

== Partition Function ==

''Classical'' Partition Function (one-component system) in a three-dimensional space: <math> Q_{NVT} </math>

:<math> Q_{NVT} = \frac{V^N}{N! \Lambda^{3N} } \int  d (R^*)^{3N} \exp \left[ - \beta U \left( V, (R^*)^{3N} \right) \right] </math>

where:

* <math> \Lambda </math> is the [[de Broglie wavelength]] (depends on the temperature)

* <math> \beta = \frac{1}{k_B T} </math>, with <math> k_B </math> being the [[Boltzmann constant]]

* <math> U </math> is the potential energy, which depends on the coordinates of the particles (and on the interaction model)

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

== Free energy and Partition Function ==

The  [[Helmholtz energy function]] is related to the canonical partition function via:

:<math> A\left(N,V,T \right) = - k_B T \log  Q_{NVT} </math>
@@ Line 5: / Line 5: @@
 * Volume, <math> V </math>
-* [[Temperature]], <math> T </math>
+* Temperature, <math> T </math>
 == Partition Function ==
-The [[partition function]], <math>Q</math>,
-for a system of <math>N</math> identical particles each of mass <math>m</math> is given by
-:<math>Q_{NVT}=\frac{1}{N!h^{3N}}\iint d{\mathbf p}^N d{\mathbf r}^N \exp \left[ - \frac{H({\mathbf p}^N,{\mathbf r}^N)}{k_B T}\right]</math>
+''Classical'' Partition Function (one-component system) in a three-dimensional space: <math> Q_{NVT} </math>
-where <math>h</math> is [[Planck constant |Planck's constant]], <math>T</math> is the [[temperature]], <math>k_B</math> is the [[Boltzmann constant]] and <math>H(p^N, r^N)</math> is the [[Hamiltonian]]
+:<math> Q_{NVT} = \frac{V^N}{N! \Lambda^{3N} } \int  d (R^*)^{3N} \exp \left[ - \beta U \left( V, (R^*)^{3N} \right) \right] </math>
-corresponding to the total energy of the system.
-For a classical  one-component system in a three-dimensional space, <math> Q_{NVT} </math>,
-is given by:
-:<math> Q_{NVT} = \frac{V^N}{N! \Lambda^{3N} } \int  d (R^*)^{3N} \exp \left[ - \beta U \left( V, (R^*)^{3N} \right) \right] ~~~~~~~~~~ \left( \frac{V}{N\Lambda^3} \gg 1 \right) </math>
 where:
-* <math> \Lambda </math> is the [[de Broglie thermal wavelength]] (depends on the temperature)
+* <math> \Lambda </math> is the [[de Broglie 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]]
 * <math> U </math> is the potential energy, which depends on the coordinates of the particles (and on the interaction model)
@@ Line 30: / Line 23: @@
 * <math> \left( R^*\right)^{3N} </math> represent the 3N position coordinates of the particles (reduced with the system size): i.e. <math> \int d (R^*)^{3N} = 1 </math>
-==See also==
+== Free energy and Partition Function ==
-*[[Ideal gas partition function]]
-==References==
+The  [[Helmholtz energy function]] is related to the canonical partition function via:
-<references/>
-[[Category:Statistical mechanics]]
+:<math> A\left(N,V,T \right) = - k_B T \log  Q_{NVT} </math>