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1、复旦量子力学讲义qmapter2 Still waters run deep.流静水深流静水深,人静心深人静心深 Where there is life,there is hope。有生命必有希望。有生命必有希望2.1 Second quantizationThe identical particles cannot be distinguished2.1 Second quantizationThe essence of the identical principle is that the state of a system should be described in terms of
2、the particle number in a certain quantum state and the many-body problem should be discussed in the particle number representation instead of the original coordinate representation2.1 Second quantizationWe need to introduce the creation and the annihilation operators to deal with various problem in
3、the many-body system2.1 Second quantizationBose system2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quant
4、izationDiscussionsThe wave function is already symmetricnk is the particle number operator of k state2.1 Second quantization2.1 Second quantization2.1 Second quantizationSecond quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantization2.1 Second quantiza
5、tionFor Fermions2.1 Second quantization2.1 Second quantization2.1 Second quantization2.2 Hartree-Fork mean field approximationKey:two-body problem“one-body problem”+“mean field”Example:Free electron gas in the metal2.2 Hartree-Fork mean field approximationScreening Coulomb potentialPositive charge b
6、ackground cancels k=0 part2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field
7、approximationSpin effect2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field approximation2.2 Hartree-Fork mean field approximation2.3 Superconductive theoryExperimental results1908K.Onnes Liquid helium1911Hg:Tc=4.2K1933Meissner effect B=01986Muller,Bednorz High TcHeat capacity Cs ex
8、p(-/kBT)energy gapIsotropic effect Tc M1/2=const.2.3 Superconductive theoryFrohlisch Hamiltonian:e-p-e interaction e-e attractionCooper pair:BCS Theory(Variational method)Variational wave function2.3 Superconductive theory2.3 Superconductive theory2.3 Superconductive theory2.3 Superconductive theory
9、2.3 Superconductive theoryBogoliubov-Valatin canonical transformation2.3 Superconductive theory2.3 Superconductive theory2.3 Superconductive theory2.3 Superconductive theory2.3 Superconductive theoryEnergy gap equation2.3 Superconductive theory2.3 Superconductive theory2.3 Superconductive theory2.3
10、Superconductive theoryStable state2.4 Landau phase transition theoryEhrenfest equation2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landau phase transition theoryVan Laue criticismCan 2nd order phase transi
11、tion exist?2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landau phase transition theoryLandau theoryIntroducing“order parameter ”2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landa
12、u phase transition theory min,stable max,instalble phase transition point2.4 Landau phase transition theory real,stable img,forbiddenA 02.4 Landau phase transition theoryLandau theory Ehrenfest equation2.4 Landau phase transition theory2.4 Landau phase transition theory2.4 Landau phase transition th
13、eory2.4 Landau phase transition theory2.5 Superfluidity theoryLandau superfluidity theoryNew idea:elementary excitation2.5 Superfluidity theoryExperiments:Superfluidity 10-510-4 cm(0)Mendelson effect-point2.5 Superfluidity theory2.5 Superfluidity theoryLandau theory2.5 Superfluidity theory2.5 Superf
14、luidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theoryBogoliubov approximate second-quantization method2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory2.5 Superfluidity theory