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苏汝铿高等量子力学讲义(英文版)Chapter2 Many Body Problem


§2.3 Superconductive theory
§2.3 Superconductive theory
§2.3 Superconductive theory
§2.3 Superconductive theory
§2.3 Superconductive theory
Energy gap equation
§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
§2.3 Superconductive theory
§2.3 Superconductive theory
ξ = k − k0
§2.3 Superconductive theory
§2.3 Superconductive theory
( E0 < E0 N )
Stable state
§2.4 Landau phase transition theory
§2.4 Landau phase transition theory
A~0 real, stable
img,forbidden
§2.4 Landau phase transition theory
Landau theory Ehrenfest equation
§2.4 Landau phase tdity theory
§2.5 Superfluidity theory
§2.5 Superfluidity theory
§2.5 Superfluidity theory
§2.5 Superfluidity theory
§2.5 Superfluidity theory
§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
§2.4 Landau phase transition theory
§2.4 Landau phase transition theory
Landau theory Introducing “order parameter η ”
µ = µ ( p , T ,η )
§2.4 Landau phase transition 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
Bose system
§2.1 Second quantization
Πni ! r r r r Φ n1 ,..., nk ,... (r1 ,...rN ) = ∑ Pϕk1 (r1 )...ϕkN (rN ) N! P
§2.1 Second quantization
A(k1 , k2 ,..., kn , t ) =
§2.3 Superconductive theory
§2.3 Superconductive theory
§2.3 Superconductive theory
§2.3 Superconductive theory
§2.3 Superconductive theory
Bogoliubov-Valatin canonical transformation
§2.1 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
§2.1 Second quantization
§2.1 Second quantization
§2.1 Second quantization
§2.1 Second quantization
Discussions The wave function is already symmetric nk is the particle number operator of k state
m≤k
§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
§2.3 Superconductive theory
Frohlisch Hamiltonian: e-p-e interaction + + Cooper pair: ak ↑ a− k ↓ 0 BCS Theory (Variational method) e-e attraction
Variational wave function
§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
1 ikr ⋅rr e 2 r e 2 ∞ π 2π ikr cosθ 1 2 Uk = ∫ e dr = ∫ ∫ ∫ e r dr sin θ dθ dϕ 0 0 0 Ω r Ω r 4π e 2 ∞ = ∫0 sin krdr Ωk
Screening Coulomb potential
Positive charge background cancels k=0 part
Chapter 2 Many 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 should be discussed in the particle number representation instead of the original coordinate representation
§2.5 Superfluidity theory
Experiments: Superfluidity 10^-5~10^-4 cm (η 0) κ ∞ Mendelson effect λ- point
§2.5 Superfluidity theory
§2.5 Superfluidity theory
§2.2 Hartree-Fork mean field approximation
§2.2 Hartree-Fork mean field approximation
§2.2 Hartree-Fork mean field approximation
Spin effect
§2.2 Hartree-Fork mean field approximation
§2.5 Superfluidity theory
§2.5 Superfluidity theory
§2.5 Superfluidity 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
§2.1 Second quantization
§2.1 Second quantization
For Fermions
§2.1 Second quantization
§2.1 Second quantization
§2.1 Second quantization
υk = ∏ (1 − 2nm )
§2.1 Second quantization
§2.1 Second quantization
§2.1 Second quantization
Second quantization
§2.1 Second quantization
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