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created: 2022-05-29 15:09:15
modified: 2022-05-29 15:22:24
Let's consider a classical physical system of particles with degrees of freedom for each particle.
The number of states for this system for lower than energies is:
Where is an infinitesimal volume piece of the dimensional phase space, is the Hamiltonian, is the Planck constant and makes the term dimensionless having no unit of measurement. The combinatorial factor is needed in case of indistinguishable particles (see indistinguishable particles for the quantum mechanical analogue), for example with ideal gas.
Number of states in an energy interval
Sometimes we might be interested in the number of states in the wide energy interval around , where .
State density
From the above definition, we can define the state density by taking the derivative of :