A general definition of the thermal wavelength for an ideal gas of particles having an arbitrary power-law relationship between energy and momentum (dispersion relationship), in any number of dimensions, can be introduced. If n is the number of dimensions, and the relationship between energy (E) and momentum (p) is given by E = a p s (with a and s being constants), then the thermal wavelength is defined as λ λ t h = h π π ( a k B T ) 1 / s [ Γ Γ ( n / 2 + 1 ) Γ Γ ( n / s + 1 ) ] 1 / n , where Γ is the Gamma function. In particular, for a 3-D (n = 3) gas of massive or massless particles we have E = p /2 m (a = 1/2 m, s = 2) and E = pc (a = c, s = 1), respectively, yielding the expressions listed in the previous sections. Note that for massive non-relativistic particles (s = 2), the expression does not depend on n. This explains why the 1-D derivation above agrees with the 3-D case.