复旦量子力学讲义qmapter2

1、Chapter 2Many Body Problem Second quantizationThe identical particles cannot be distinguished 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 should be dis

2、cussed in the particle number representation instead of the original coordinate representation Second quantizationWe need to introduce the creation and the annihilation operators to deal with various problem in the many-body system Second quantizationBose system Second quantization Second quantizati

3、on Second quantization Second quantization Second quantization Second quantization Second quantization Second quantization Second quantization Second quantization Second quantizationDiscussionsThe wave function is already symmetricnk is the particle number operator of k state Second quantization Sec

4、ond quantization Second quantizationSecond quantization Second quantization Second quantization Second quantization Second quantization Second quantizationFor Fermions Second quantization Second quantization Second quantization Hartree-Fork mean field approximationKey: two-body problem “one-body pro

5、blem” + “mean field”Example: Free electron gas in the metal Hartree-Fork mean field approximationScreening Coulomb potentialPositive charge background cancels k=0 part Hartree-Fork mean field approximation Hartree-Fork mean field approximation Hartree-Fork mean field approximation Hartree-Fork mean

6、field approximation Hartree-Fork mean field approximation Hartree-Fork mean field approximation Hartree-Fork mean field approximationSpin effect Hartree-Fork mean field approximation Hartree-Fork mean field approximation Hartree-Fork mean field approximation Superconductive theoryExperimental result

7、s1908K.Onnes Liquid helium1911Hg: Tc=4.2K1933Meissner effect B=01986Muller, Bednorz High TcHeat capacity Cs exp(-/kBT) energy gapIsotropic effect Tc M1/2=const. Superconductive theoryFrohlisch Hamiltonian: e-p-e interaction e-e attractionCooper pair:BCS Theory (Variational method)Variational wave fu

8、nction Superconductive theory Superconductive theory Superconductive theory Superconductive theory Superconductive theoryBogoliubov-Valatin canonical transformation Superconductive theory Superconductive theory Superconductive theory Superconductive theory Superconductive theoryEnergy gap equation S

9、uperconductive theory Superconductive theory Superconductive theory Superconductive theoryStable state Landau phase transition theoryEhrenfest equation Landau phase transition theory Landau phase transition theory Landau phase transition theory Landau phase transition theory Landau phase transition

10、theoryVan Laue criticismCan 2nd order phase transition exist? Landau phase transition theory Landau phase transition theory Landau phase transition theory Landau phase transition theoryLandau theoryIntroducing “order parameter ” Landau phase transition theory Landau phase transition theory Landau ph

11、ase transition theory Landau phase transition theory min, stable max,instalble phase transition point Landau phase transition theory real, stable img,forbiddenA 0 Landau phase transition theoryLandau theory Ehrenfest equation Landau phase transition theory Landau phase transition theory Landau phase

12、 transition theory Landau phase transition theory Superfluidity theoryLandau superfluidity theoryNew idea: elementary excitation Superfluidity theoryExperiments:Superfluidity 10-510-4 cm (0)Mendelson effect- point Superfluidity theory Superfluidity theoryLandau theory Superfluidity theory Superfluidity theory Superfluidity theory Superfluidity theory Superfluidity theory Superfluidity theory Superfluidity theory Superfluidity theoryBogoliubov approximate second-quantization method Superfluid