Cheat sheets/Statistical mechanics

Statistical mechanics is a branch of mathematical physics that studies, using probability theory, the average behaviour of a mechanical system where the state of the system is uncertain. A common use of statistical mechanics is in explaining the thermodynamic behaviour of large systems.

Thermal wavelength

$\lambda =\frac{h}{\sqrt{2\pi m{k}_{B}T}}=h\sqrt{\frac{\beta }{2\pi m}}=\hslash \sqrt{\frac{2\pi \beta }{m}}$

$\frac{1}{\lambda }=\frac{\sqrt{2\pi m{k}_{B}T}}{h}$

Partition function

Canonical: (in 3d)

$Z=\int \prod _{i=1}^N\frac{d^3{q}_i{d}^3{p}_i}{h^3}{e}^{-\beta \frac{p_i^2}{2m}}{e}^{-\beta U(q_i)}=\int \prod _{i=1}^N\frac{d^3{q}_i{d}^3{p}_i}{h^3}{e}^{-\beta H}$

See Also

• School of Physics
• Template:Thermodynamics

Template:Commons cat