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1、Chapter 2Many Body Problem122.1 Second quantizationThe identical particles cannot be distinguished32.1 Second quantizationThe essence of the identical principle is that the state of a system should be described in terms of the particle number in a certain quantum state and the many-body problem shou
2、ld be discussed in the particle number representation instead of the original coordinate representation42.1 Second quantizationWe need to introduce the creation and the annihilation operators to deal with various problem in the many-body system52.1 Second quantizationBose system62.1 Second quantizat
3、ion72.1 Second quantization82.1 Second quantization92.1 Second quantization102.1 Second quantization112.1 Second quantization122.1 Second quantization132.1 Second quantization142.1 Second quantization152.1 Second quantization162.1 Second quantizationDiscussionsThe wave function is already symmetricn
4、k is the particle number operator of k state172.1 Second quantization182.1 Second quantization192.1 Second quantizationSecond quantization202.1 Second quantization212.1 Second quantization222.1 Second quantization232.1 Second quantization242.1 Second quantizationFor Fermions252.1 Second quantization
5、262.1 Second quantization272.1 Second quantization282.2 Hartree-Fork mean field approximationKey: two-body problem “one-body problem” + “mean field”Example: Free electron gas in the metal292.2 Hartree-Fork mean field approximationScreening Coulomb potentialPositive charge background cancels k=0 part
6、302.2 Hartree-Fork mean field approximation312.2 Hartree-Fork mean field approximation322.2 Hartree-Fork mean field approximation332.2 Hartree-Fork mean field approximation342.2 Hartree-Fork mean field approximation352.2 Hartree-Fork mean field approximation362.2 Hartree-Fork mean field approximatio
7、nSpin effect372.2 Hartree-Fork mean field approximation382.2 Hartree-Fork mean field approximation392.2 Hartree-Fork mean field approximation402.3 Superconductive theory412.3 Superconductive theoryFrohlisch Hamiltonian: e-p-e interaction e-e attractionCooper pair:BCS Theory (Variational method)Varia
8、tional wave function422.3 Superconductive theory432.3 Superconductive theory442.3 Superconductive theory452.3 Superconductive theory462.3 Superconductive theoryBogoliubov-Valatin canonical transformation472.3 Superconductive theory482.3 Superconductive theory492.3 Superconductive theory502.3 Superco
9、nductive theory512.3 Superconductive theoryEnergy gap equation522.3 Superconductive theory532.3 Superconductive theory542.3 Superconductive theory552.3 Superconductive theoryStable state562.4 Landau phase transition theoryEhrenfest equation572.4 Landau phase transition theory582.4 Landau phase trans
10、ition theory592.4 Landau phase transition theory602.4 Landau phase transition theory612.4 Landau phase transition theoryVan Laue criticismCan 2nd order phase transition exist?622.4 Landau phase transition theory632.4 Landau phase transition theory642.4 Landau phase transition theory652.4 Landau phas
11、e transition theoryLandau theoryIntroducing “order parameter ” 662.4 Landau phase transition theory672.4 Landau phase transition theory682.4 Landau phase transition theory692.4 Landau phase transition theory min, stable max,instalble phase transition point702.4 Landau phase transition theory real, s
12、table img,forbiddenA 0712.4 Landau phase transition theoryLandau theory Ehrenfest equation722.4 Landau phase transition theory732.4 Landau phase transition theory742.4 Landau phase transition theory752.4 Landau phase transition theory762.5 Superfluidity theoryLandau superfluidity theoryNew idea: ele
13、mentary excitation772.5 Superfluidity theoryExperiments:Superfluidity 10-510-4 cm (0)Mendelson effect- point782.5 Superfluidity theory792.5 Superfluidity theoryLandau theory802.5 Superfluidity theory812.5 Superfluidity theory822.5 Superfluidity theory832.5 Superfluidity theory842.5 Superfluidity the
14、ory852.5 Superfluidity theory862.5 Superfluidity theory872.5 Superfluidity theoryBogoliubov approximate second-quantization method882.5 Superfluidity theory892.5 Superfluidity theory902.5 Superfluidity theory912.5 Superfluidity theory922.5 Superfluidity theory932.5 Superfluidity theory942.5 Superfluidity theory952.5 Superfluidity theory962.5 Superfluidity theory972.5 Superfluidity theory982.5 Superfluidity theory99100
