量子力學講義(第三卷)-微擾演化

Preface
1. Basics of Kinematics and Dynamics
1.1 Brief review of basic kinematics
1.2 Bohr's principle of complementarity
1.2.1 Complementary observables
1.2.2 Algebraic completeness
1.2.3 Bohr's principle. Technical formulation
1.2.4 Composite degrees of freedom
1.2.5 The limit N → ∞. Symmetric case
1.2.6 The limit N → ∞. Asymmetric case
1.2.7 Bohr's principle. Quantum indeterminism
1.3 Brief review of basic dynamics
1.3.1 Equations of motion
1.3.2 Time transformation functions
1.4 Schwinger's quantum action principle
1.4.1 An example: Constant force
1.4.2 Insertion: Varying an exponential function
1.4.3 Time-independent Hamilton operator
2. Time-Dependent Perturbations
2.1 Born series
2.2 Scattering operator
2.3 Dyson series
2.4 Fermi's golden rule
2.5 Photon emission by a "two-level atom"
2.5.1 Golden-rule treatment
2.5.2 A more detailed treatment
2.5.3 An exact treatment
2.6 Driven two-level atom
2.6.1 Schrdinger equation
2.6.2 Resonant drive
2.6.3 Periodic drive
2.6.4 Very slow drive. Adiabatic evolution
2.7 Adiabatic population transfer
2.8 Equation of motion for the unitary evolution operator
3. Scattering
3.1 Probability density, probability current density
3.2 One-dimensional prelude: Forces scatter
3.3 Scattering by a localized potential
3.3.1 Golden-rule approximation
3.3.2 Example: Yukawa potential
3.3.3 Rutherford cross section as a limit
3.4 Lippmann-Schwinger equation
3.4.1 Born approximation
3.4.2 Transition operator
3.4.3 Optical theorem
3.4.4 Example of an exact solution
3.5 Partial waves
3.6 s-wave scattering
4. Angular Momentum
4.1 Spin
4.2 Addition of two angular momenta
4.2.1 Two spin- systems
4.2.2 Total angular momentum of an electron
5. External Magnetic Field
5.1 Electric charge in a magnetic field
5.2 Electron in a homogeneous magnetic field
6. Indistinguishable Particles
6.1 Indistinguishability
6.2 Bosons and fermions
6.3 Scattering of two indistinguishable particles
6.4 Two-electron atoms
6.4.1 Variational estimate for the ground state
6.4.2 Perturbative estimate for the first excited state
6.4.3 Self-consistent single-electron wave functions
6.5 A glimpse at many-electron atoms
Index