qm2_chapter2.ppt

1、Chapter 2Many Body Problem,2.1 Second quantization,The identical particles cannot be distinguished,2.1 Second quantization,The 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 sho

2、uld be discussed in the particle number representation instead of the original coordinate representation,2.1 Second quantization,We need to introduce the creation and the annihilation operators to deal with various problem in the many-body system,2.1 Second quantization,Bose system,2.1 Second quanti

3、zation,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,Discussions The wave function is already symmetric nk

4、 is the particle number operator of k state,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,2.1 Second quantization,For Fermions,2.1 Second quantization,2.1 Sec

5、ond quantization,2.1 Second quantization,2.2 Hartree-Fork mean field approximation,Key: two-body problem “one-body problem” + “mean field” Example: Free electron gas in the metal,2.2 Hartree-Fork mean field approximation,Screening Coulomb potential,Positive charge background cancels k=0 part,2.2 Har

6、tree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,Spin effect,2

7、.2 Hartree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,2.2 Hartree-Fork mean field approximation,2.3 Superconductive theory,2.3 Superconductive theory,Frohlisch Hamiltonian: e-p-e interaction e-e attraction Cooper pair: BCS Theory (Variational method),Variational wave fun

8、ction,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Superconductive theory,Bogoliubov-Valatin canonical transformation,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Sup

9、erconductive theory,Energy gap equation,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Superconductive theory,2.3 Superconductive theory,Stable state,2.4 Landau phase transition theory,Ehrenfest equation,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.4 Landau phas

10、e transition theory,2.4 Landau phase transition theory,2.4 Landau phase transition theory,Van Laue criticism Can 2nd order phase transition exist?,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.4 Landau phase transition theory,Landau theory

11、 Introducing “order parameter ”,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.4 Landau phase transition theory,min, stable max,instalble phase transition point,2.4 Landau phase transition theory,real, stable img,forbidden,A 0,2.4 Landau ph

12、ase transition theory,Landau theory Ehrenfest equation,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.4 Landau phase transition theory,2.5 Superfluidity theory,Landau superfluidity theory New idea: elementary excitation,2.5 Superfluidity th

13、eory,Experiments: Superfluidity 10-510-4 cm (0) Mendelson effect - point,2.5 Superfluidity theory,2.5 Superfluidity theory,Landau theory,2.5 Superfluidity theory,2.5 Superfluidity theory,2.5 Superfluidity theory,2.5 Superfluidity theory,2.5 Superfluidity theory,2.5 Superfluidity theory,2.5 Superfluidity theory,2.5 Superfluidity theory,Bogoliubov approximate second-quantization method,2.5 Superfluidity theory,2.5 Superfluidity theory,2.5 Superflu