General Definition of The Thermal Wavelength
A general definition of the thermal wavelength for an ideal quantum gas in any number of dimensions and for a generalized relationship between energy and momentum (dispersion relationship) has been given by Yan (Yan 2000). It is of practical importance, since there are many experimental situations with different dimensionality and dispersion relationships. If n is the number of dimensions, and the relationship between energy (E) and momentum (p) is given by:
where a and s are constants, then the thermal wavelength is defined as:
where Γ is the Gamma function. For example, in the usual case of massive particles in a 3-D gas we have n=3, and E = p2/2m which gives the above results for massive particles. For massless particles in a 3-D gas, we have n=3 , and E=pc which gives the above results for massless particles.
Read more about this topic: Thermal De Broglie Wavelength
Famous quotes containing the words general and/or definition:
“To have in general but little feeling, seems to be the only security against feeling too much on any particular occasion.”
—George Eliot [Mary Ann (or Marian)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)