7.7 Magnetism of the electron gas 7.7.1 Paramagnetic response of the electron gas 7.7.2 Diamagnetic response of the electron gas 7.7.3 The RKKY interaction 7.8 Excitations in the electron gas 7.9 Spin-density waves 7.10 The Kondo effect 7.11 The Hubbard model 7.12 Neutron stars 4.Teaching method Teaching:Group Discussion:Autodidacticism under the guidance of the teacher 5.Comments Carefully prepare lessons,prepare students and make preparations before class:In the teaching process,we pay attention to cultivating students'creative thinking,take students as the main body and enhance students'sense of participation:Corresponding exercises and supplementary exercises after class. Problem (7.1)(a)Show that the paramagnetic susceptibility of a nondegenerate electron gas containing N electrons is identical to that of N independent localized electrons whose orbital motion is quenched. (b)Consider a semiconductor with 3 x 1022 electrons per cubic metre in its conduction band and an effective mass m*=0.lme.Estimate the temperature below which the magnetic susceptibility is independent of temperature.Belo this tem erature,calculate the magnitude of the Pauli paramagnetism and the Landau diamagnetism (7.2)Show that the Fourier transform of the Fermi sphere is related to a function related to the RKKY function in eqn 7.89,namely that d3keikr Jk<k好 3[sin kpr-ker cos kpr](7.95) 4π7.7 Magnetism of the electron gas 7.7.1 Paramagnetic response of the electron gas 7.7.2 Diamagnetic response of the electron gas 7.7.3 The RKKY interaction 7.8 Excitations in the electron gas 7.9 Spin-density waves 7.10 The Kondo effect 7.11 The Hubbard model 7.12 Neutron stars 4. Teaching method Teaching; Group Discussion; Autodidacticism under the guidance of the teacher 5. Comments Carefully prepare lessons, prepare students and make preparations before class; In the teaching process, we pay attention to cultivating students' creative thinking, take students as the main body and enhance students' sense of participation; Corresponding exercises and supplementary exercises after class. Problem (7.1) (a) Show that the paramagnetic susceptibility of a nondegenerate electron gas containing N electrons is identical to that of N independent localized electrons whose orbital motion is quenched. (b) Consider a semiconductor with 3 x 1022 electrons per cubic metre in its conduction band and an effective mass m* = 0.lme. Estimate the temperature below which the magnetic susceptibility is independent of temperature. Below this temperature, calculate the magnitude of the Pauli paramagnetism and the Landau diamagnetism (7.2) Show that the Fourier transform of the Fermi sphere is related to a function related to the RKKY function in eqn 7.89, namely that