Only results and calculation formulas are shown on this page. You can find the derivations for them and other useful sources on the bottom of this page.

1-D Wave Equation | 2-D Wave Equation | 3-D Wave Equation | Calculation formula | |

Eigenfunction solutions | - | |||

Dispersion relation | - | |||

Density of states, D(k) | ||||

Density of states, D(ω) | ||||

Density of states, D(λ) | ||||

Density of states, D(E) | ||||

Intensity distribution, I(λ) | ||||

Wien's law | ||||

Stefan - Boltzmann law | ||||

Internal energy distribution, u(λ) | ||||

Internal energy | ||||

Helmholtz free energy | ||||

Entropy | ||||

Specific heat | ||||

Pressure | ||||

c = velocity of propagation. Photons: c = 299792458 m/s.u = wave function.k = wave number.= wave vector. Ω = the wave's frequency.p = number of polarizations. Photons: p = 2, Phonons: p = 3.= the area of the surface in reciprocal space (k-space) with given k. V = the volume of the brillouin zone in the reciprocal space. ^{rez}. V = volume of our box. . λ = wavelength.E = energy.h = Planck constant. h = 6.62606896E-34 Js.= reduced Planck constant. . k = Boltzmann constant. _{B}k = 1.3806504E-23 J/K._{B}= the vector pointing out of the infinitesimally small area dA. Ω = the solid angle of the space. In 3D, _{R}Ω = 4π._{R}Ω = the solid angle of the half-space._{R/2}= the unitary vector pointing in the direction specified by Ω.λ = the peak wavelength of the intensity._{max}T = temperature. . ζ = the Riemann Zeta function._{(s)} |

How to derive these results

Wikipedia article about the Stefan Boltzmann law

Wikipedia article about Planck's Black Body radiation law

The Bose-Einstein distribution in short

German Wikipedia article containing formulas on Planck's Black Body radiation law

German Wikipedia article about Planck's Black Body radiation law