Thermal de Broglie Wavelength - General Definition of The Thermal Wavelength

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.