Raghuveer parthasarathy university of oregon physics 353 spring 2008 notes on the sommerfeld expansion, applied to n start with the relation ndf d0. Pdf how sommerfeld extended bohrs model of the atom. Notes on the sommerfeld expansion for bloch electrons. In class you have seen that the sommerfeld expansion is a useful tool for calculating the lowt behavior of ideal. A sommerfeld expansion is an approximation method developed by arnold sommerfeld for a. The fermi liquid theory approach gives the result for heat capacity using sommerfeld expansion with density of states for 1d case n. It is useful to calculate physical observables of degenerate fermi gases. Ganesh the drude model is inadequate in many respects, e. Pdf sommerfeld s extension of bohrs atomic model was motivated by the quest for a theory of the zeeman and stark effects. The sommerfeld expansion and the calculation of properties near the fermi level 2. Physically, the integrals represent statistical averages using the fermidirac distribution. Then the sommerfeld expansion for the fermidirac integral of order j can be evaluated by.
We saw in the previous section that the fermi energy, is determined by the equation 8. A good source for the density of states of different materials is springer materials. Results of the sct in particular the behavior of electrons near the band edge 5. Notes on the sommerfeld expansion university of oregon. Sommerfeld proposed that the electrons in a metal can be described by a free electron gas. Pdf analytical computation of generalized fermidirac integrals. Luttinger liquid problem 1 problem 2 physics montana state. Many of these errors occur because the electrons velocity and energy are deduced from a classical distribution. A sommerfeld expansion is an approximation method developed by arnold sommerfeld for a certain class of integrals which are common in condensed matter and statistical physics. Modern computers allow to do this e ciently numerically. For example, if 12, one needs to substitute z z12 and 12 in the above to obtain i for 12 2 3 32.
Analytical computation of generalized fermidirac integrals by truncated sommerfeld expansions. Let us examine the conduction electrons in a metal in slightly more detail. In 1912 sommerfeld introduced his radiation condition to ensure the uniqueness of the solution of. In particular, let us try to obtain a more exact expression for the electronic specific heat. Marx available to tu graz students through the tu graz library. Physically, the integrals represent statistical averages using the fermidirac distribution when the inverse temperature is a large quantity, the integral can be expanded in terms of as. This short document provides an overview of the current state of affairs concerning the forces excerpted by electromagnetic fields. Notes on the sommerfeld expansion for bloch electrons prof. This expansion is known as the sommerfeld expansion, after its inventor, arnold sommerfeld. This document will provide a proof for the sommerfeld expansion. Advancedsolidstatephysicsstudentproject ss20 sommerfeldexpansion use the sommerfeld expansion to calculate the temperature dependence of the chemical potentialinternal energy in onetwo. Calculating the electronic contribution to the heat capacity of a metal at moderate temperatures. Bakkelaureatsarbeit sommerfeld expansion for various metals.