What are fundamental assumptions of FD Statistics?
1. Indistinguishability : Particles of the same type are indistinguishable from each other. This means that you can't tell one electron from another identical electron.
2. Pauli Exclusion Principle : No two electrons (or other fermions) can occupy the same quantum state simultaneously. This is the basis for the "exclusion" part of Fermi-Dirac statistics.
3. Quantum States : Each particle can be in a unique quantum state defined by its energy, momentum, and other quantum numbers.
The probability of finding a particle in a particular quantum state follows the Fermi-Dirac distribution function:
\[ f(E) = \frac{1}{e^{(E - \mu) / kT} + 1} \]
where :
- \( E \) is the energy of the state.
- \( \mu \) is the chemical potential, which represents the energy level below which most states are occupied at a given temperature.
- \( k \) is the Boltzmann constant.
- \( T \) is the temperature.
This distribution function shows how the probability of finding a particle in a state changes with energy and temperature. At very low temperatures, most states are occupied, leading to the phenomenon of Fermi degeneracy. As temperature increases, more states become accessible.
Also Read : Write Maxwell's four Thermodynamic Relations.
Also Read : What is Rigid Rotator? Write Schrodinger's Equation for it and obtain Eigen values and Eigen functions.
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