Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
quantum_canonical_partition_function [2016/03/03 13:32]
nikolaj
quantum_canonical_partition_function [2016/03/03 13:33]
nikolaj
Line 13: Line 13:
 Generally, material physics of finite (i.e. non-zero) temperature derives its macroscopic relations from small scale considerations. All observables are essentially determined by the relation between the possible microscopic states and their energy, which makes evaluation of the partition function possible. This is why the computation of energy levels $\varepsilon_r$ or dispersion relations $\hbar\omega({\bf k})$ are of central importance. Quantum mechanically,​ this requires computing eigenvalues of the Hamiltonian. Generally, material physics of finite (i.e. non-zero) temperature derives its macroscopic relations from small scale considerations. All observables are essentially determined by the relation between the possible microscopic states and their energy, which makes evaluation of the partition function possible. This is why the computation of energy levels $\varepsilon_r$ or dispersion relations $\hbar\omega({\bf k})$ are of central importance. Quantum mechanically,​ this requires computing eigenvalues of the Hamiltonian.
  
->todo: $\langle A\rangle ​:= \dfrac{\mathrm{tr}(\mathrm e^{-\beta H}A)}{\mathrm{tr}(\mathrm e^{-\beta H})} = \dfrac{1}{Z(\beta)} \mathrm{tr}({\mathrm e}^{-\beta H}A) $+>​todo: ​Ensemble average 
 +>$\langle A\rangle_H ​:= \dfrac{\mathrm{tr}(\mathrm e^{-\beta H}A)}{\mathrm{tr}(\mathrm e^{-\beta H})} = \dfrac{1}{Z(\beta)} \mathrm{tr}({\mathrm e}^{-\beta H}A) $
  
 ----- -----
Link to graph
Log In
Improvements of the human condition