Bose-Einstein Distribution Plotter
Bose-Einstein Distribution Plotter visualizes boson occupancy vs. energy for given temperature and chemical potential, aiding quantum and statistical physics studies.
Formulas Used in Bose-Einstein Distribution Plotter
The plotter uses the following formula for the Bose-Einstein distribution:
Bose-Einstein Distribution:
\\[ f(E) = \frac{1}{e^{(E – \mu)/(k_B T)} – 1} \\]Where:
- \\( f(E) \\): Average number of bosons in a state (dimensionless, \\( \geq 0 \\))
- \\( E \\): Energy (eV)
- \\( \mu \\): Chemical potential (eV)
- \\( k_B \\): Boltzmann constant (\\( 8.617333262 \times 10^{-5} \, \text{eV/K} \\))
- \\( T \\): Temperature (K)
Example Calculations
Example 1: Photons at Room Temperature
Input: Temperature = 300 K, Chemical Potential = 0 eV, Energy Range = 0.5 eV
Result: Occupancy at E = 0.1 eV: 0.021, Plot Range: [0, 0.5] eV
Example 2: Low Temperature Bosons
Input: Temperature = 10 K, Chemical Potential = -0.01 eV, Energy Range = 0.5 eV
Result: Occupancy at E = 0 eV: 8.63e-6, Plot Range: [0, 0.5] eV
Example 3: Wide Energy Range
Input: Temperature = 300 K, Chemical Potential = -0.1 eV, Energy Range = 1 eV
Result: Occupancy at E = 0 eV: 0.021, Plot Range: [0, 1] eV