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1、第1页/共100页2.1 Second quantizationThe identical particles cannot be distinguished第2页/共100页2.1 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 should be discu
2、ssed in the particle number representation instead of the original coordinate representation第3页/共100页2.1 Second quantizationWe need to introduce the creation and the annihilation operators to deal with various problem in the many-body system第4页/共100页2.1 Second quantizationBose system第5页/共100页2.1 Sec
3、ond quantization第6页/共100页2.1 Second quantization第7页/共100页2.1 Second quantization第8页/共100页2.1 Second quantization第9页/共100页2.1 Second quantization第10页/共100页2.1 Second quantization第11页/共100页2.1 Second quantization第12页/共100页2.1 Second quantization第13页/共100页2.1 Second quantization第14页/共100页2.1 Second qua
4、ntization第15页/共100页2.1 Second quantizationDiscussionsThe wave function is already symmetricnk is the particle number operator of k state第16页/共100页2.1 Second quantization第17页/共100页2.1 Second quantization第18页/共100页2.1 Second quantizationSecond quantization第19页/共100页2.1 Second quantization第20页/共100页2.1
5、 Second quantization第21页/共100页2.1 Second quantization第22页/共100页2.1 Second quantization第23页/共100页2.1 Second quantizationFor Fermions第24页/共100页2.1 Second quantization第25页/共100页2.1 Second quantization第26页/共100页2.1 Second quantization第27页/共100页2.2 Hartree-Fork mean field approximationKey:two-body proble
6、m“one-body problem”+“mean field”Example:Free electron gas in the metal第28页/共100页2.2 Hartree-Fork mean field approximationScreening Coulomb potentialPositive charge background cancels k=0 part第29页/共100页2.2 Hartree-Fork mean field approximation第30页/共100页2.2 Hartree-Fork mean field approximation第31页/共1
7、00页2.2 Hartree-Fork mean field approximation第32页/共100页2.2 Hartree-Fork mean field approximation第33页/共100页2.2 Hartree-Fork mean field approximation第34页/共100页2.2 Hartree-Fork mean field approximation第35页/共100页2.2 Hartree-Fork mean field approximationSpin effect第36页/共100页2.2 Hartree-Fork mean field app
8、roximation第37页/共100页2.2 Hartree-Fork mean field approximation第38页/共100页2.2 Hartree-Fork mean field approximation第39页/共100页2.3 Superconductive theoryExperimental results1908K.Onnes Liquid helium1911Hg:Tc=4.2K1933Meissner effect B=01986Muller,Bednorz High TcHeat capacity Cs exp(-/kBT)energy gapIsotrop
9、ic effect Tc M1/2=const.第40页/共100页2.3 Superconductive theoryFrohlisch Hamiltonian:e-p-e interaction e-e attractionCooper pair:BCS Theory(Variational method)Variational wave function第41页/共100页2.3 Superconductive theory第42页/共100页2.3 Superconductive theory第43页/共100页2.3 Superconductive theory第44页/共100页2
10、.3 Superconductive theory第45页/共100页2.3 Superconductive theoryBogoliubov-Valatin canonical transformation第46页/共100页2.3 Superconductive theory第47页/共100页2.3 Superconductive theory第48页/共100页2.3 Superconductive theory第49页/共100页2.3 Superconductive theory第50页/共100页2.3 Superconductive theoryEnergy gap equat
11、ion第51页/共100页2.3 Superconductive theory第52页/共100页2.3 Superconductive theory第53页/共100页2.3 Superconductive theory第54页/共100页2.3 Superconductive theoryStable state第55页/共100页2.4 Landau phase transition theoryEhrenfest equation第56页/共100页2.4 Landau phase transition theory第57页/共100页2.4 Landau phase transiti
12、on theory第58页/共100页2.4 Landau phase transition theory第59页/共100页2.4 Landau phase transition theory第60页/共100页2.4 Landau phase transition theoryVan Laue criticismCan 2nd order phase transition exist?第61页/共100页2.4 Landau phase transition theory第62页/共100页2.4 Landau phase transition theory第63页/共100页2.4 La
13、ndau phase transition theory第64页/共100页2.4 Landau phase transition theoryLandau theoryIntroducing“order parameter ”第65页/共100页2.4 Landau phase transition theory第66页/共100页2.4 Landau phase transition theory第67页/共100页2.4 Landau phase transition theory第68页/共100页2.4 Landau phase transition theory min,stabl
14、e max,instalble phase transition point第69页/共100页2.4 Landau phase transition theory real,stable img,forbiddenA 0第70页/共100页2.4 Landau phase transition theoryLandau theory Ehrenfest equation第71页/共100页2.4 Landau phase transition theory第72页/共100页2.4 Landau phase transition theory第73页/共100页2.4 Landau phas
15、e transition theory第74页/共100页2.4 Landau phase transition theory第75页/共100页2.5 Superfluidity theoryLandau superfluidity theoryNew idea:elementary excitation第76页/共100页2.5 Superfluidity theoryExperiments:Superfluidity 10-510-4 cm(0)Mendelson effect-point第77页/共100页2.5 Superfluidity theory第78页/共100页2.5 Su
16、perfluidity theoryLandau theory第79页/共100页2.5 Superfluidity theory第80页/共100页2.5 Superfluidity theory第81页/共100页2.5 Superfluidity theory第82页/共100页2.5 Superfluidity theory第83页/共100页2.5 Superfluidity theory第84页/共100页2.5 Superfluidity theory第85页/共100页2.5 Superfluidity theory第86页/共100页2.5 Superfluidity the
17、oryBogoliubov approximate second-quantization method第87页/共100页2.5 Superfluidity theory第88页/共100页2.5 Superfluidity theory第89页/共100页2.5 Superfluidity theory第90页/共100页2.5 Superfluidity theory第91页/共100页2.5 Superfluidity theory第92页/共100页2.5 Superfluidity theory第93页/共100页2.5 Superfluidity theory第94页/共100页2.5 Superfluidity theory第95页/共100页2.5 Superfluidity theory第96页/共100页2.5 Superfluidity theory第97页/共100页2.5 Superfluidity theory第98页/共100页第99页/共100页感谢您的观看！第100页/共100页