Quick Index on Quantum Mechanics

Quick Index on Quantum Mechanics

Basics of quantum mechanics

 * Experiments

Black body radiation, Su P.2 & P.6, Su (S) ? Photoelectric effect, Su P.3 & P.7 Balmer Spectra and Bohr model of the atom, Su P.3 & P.9 Compton Effect, Su P.7 Electron Diffraction Su P.13 Heat Capacity, Su P.4 & Su (S) P.178 P.182


 * Wave-particle duality


 * Wave package

Sakurai P.57, Su P.14


 * Uncertainty principle

Position momentum, Sakurai P.34 Energy time, Sakurai P.79-P.80


 * Probability and measurement


 * Wave function interpretation

Sakurai P.101, Su P.19

Sakurai P.23

Mathematical structure of quantum mechanics

 * Linear operator

Sakurai P.15 (1.2.22), A brief summary, Weinberg P.49, Sakurai P.10 Section 1.2


 * Hermit operator and observable

Sakurai P.15 (1.2.24-25), Su P.95


 * Hilbert space

Sakurai P.18


 * Eigen-state and eigen-value

Sakurai P.17 Section 1.3


 * Poisson bracket and commutator


 * Path integral

Sakurai P.118

Schrodinger's equation

 * Derivation

Sakurai

Translation P.44 -> Generator -> Generating function of Classical Mechanics (1.6.29) -> Classical Poisson bracket correspondence (1.6.47) -> Momentum and Position Operator in Coordinate Representation (1.7.17) -> Time Evolution Operator (2.1.15) -> Hamiltonian -> Schrodinger Eq.

Su

Plane Wave -> Momentum and Position Operator -> Hamilton Operator -> Schrodinger Eq.


 * Boundary conditions

Sakurai P.339, Su (S) P.158


 * One-dimensional potential

Su P.24, P.40, Sakurai P.449


 * Harmonic oscillator

Sakurai P.89, Su P.35 & P.151


 * Three-dimensional problem: central potential, radial equation

Su P.57, Sakurai P.450


 * Hydrogen atom

Su P.62, Sakurai P.454


 * Three-dimensional oscillator

Su P.72

Many body problem

 * Identical particles

Sakurai P.357, Su P.343

Angular momentum

 * Orbital angular momentum

Orbital angular momentum, Sakurai P.196, Eigenvalue of angular momentum, Sakurai P.189


 * Addition of angular momentum, Sakurai P.203

Electromagnetic interaction

 * Interaction between electron and EM field

Gauge invariance of EOM, Sakurai P.130 (Gauge invariance with external field is studied in terms of Langrange in QFT) Linear Stark Effect, Sakurai P.302 (Dipole interaction) Fine Structure, Sakurai P.304 (Spin magnetic momentum interaction are put in by hand instead of derived from Dirac Eq.) Hyperfine Structure do átom de hidrogênio, Landau P.498 Stern-Geralch Experiment, Sakurai P.2 Zeeman effect, Sakurai P.308


 * Atom radiation (Interação de elétrons com o campo eletromagnético em termos de fotos)

Full interaction in transverse (radiation) guage, Sakurai A P.301 + (2.95) derived due to the relative nature of EOM, Su P.423 Dipole approximation, Transições proibadas, emissão espontânea Sakurai P.337, Sakurai A P.37 Photoelectric Effect, Sakurai P.339 Rayleigh Scattering (AA term, elastic scattering of light, long wave length), Thomson Scattering(short wave length) and Raman Effect(non-elastic), Sakurai A P.47 Lamb Shift (Self energy of electron) Sakurai A P.64, Mandl P.

Symmetries

 * Laws of conservation

Sakurai P.249


 * Translation

Sakurai P.261


 * Translation e space-time inversion

Sakurai P.251 & P.266, Weinberg P.

Perturbation theory

 * Time independent perturbation theory

Sakurai P.285


 * Degeneracy

Sakurai P.298


 * Variacional principle

Sakurai P.313


 * WKB approximation

Sakurai P.104, Su P.216


 * Two-state system

Sakurai P.320


 * Time dependent perturbation theory, transition probability, Fermi's Golden rule

Sakurai P.326

Collision theory

 * Cross section

Sakurai P.385


 * S-matrix

Weinberg P.

Su P.320


 * Colisões estacionárias

Sakurai P.386


 * Central potential

Sakurai P.399

Problems in Low Dimensional Space

 * Anyon in fractional quantum Hall effect
 * 2-dimensional superconductivity of cuprate superconductors
 * (The less) singularity in 2-dimensional Green function
 * General solutions of Laplace equation in 2 and 3 dimensional space