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m →Thermodynamic properties in 3D: T and k previously defined |
NickHattrup (talk | contribs) m I believe argument for potential of an ideal gas was flipped, if potential was infinite at all other positions, then the integral simplify to a dirac delta function at r = r_gas but as it is a point mass this integral is 0. |
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\end{align} </math>Integrating the n-particle density gives the [[Permutation|permutation factor]] <math> _NP_n</math>, counting the number of ways one can sequentially pick particles to place at the <math> n</math> positions out of the total <math> N</math> particles. Now let's turn to how we interpret this functions for different values of <math> n</math>.
For <math>n=1</math>, we have the one-particle density. For a crystal it is a periodic function with sharp maxima at the lattice sites. For a non-interacting gas, it is independent of the position <math>\textstyle \mathbf{r}_1</math> and equal to the overall number density, <math>\rho</math>, of the system. To see this first note that <math>U_N =
:<math> Z_N = \prod_{i=1}^N\int\mathrm{d}^3\mathbf{r}_i \ 1=V^N</math>
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