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Quantum Mechanics

  • PHYS 130B Lecture Notes
  • Chapter 1: Qubit
    • 1.1 States and Observables
      • 1.1.1 What is a Qubit
      • 1.1.2 State and Representation
      • 1.1.3 Hermitian Operators
    • 1.2 Measurement
      • 1.2.1 Measurement Postulate
      • 1.2.2 Uncertainty and Incompatibility
      • 1.2.3 Measurement Operators
    • 1.3 Time Evolution
      • 1.3.1 Unitary Evolution
      • 1.3.2 Schrödinger Picture
      • 1.3.3 Heisenberg Picture
  • Chapter 2: Identical Particles
    • 2.1 Bosons and Fermions
      • 2.1.1 Tensor Product
      • 2.1.2 Symmetrization
      • 2.1.3 Second Quantization
    • 2.2 Angular Momentum
      • 2.2.1 Angular Momentum Algebra
      • 2.2.2 Spin Representations
      • 2.2.3 Addition of Angular Momenta
    • 2.3 Anyons
      • 2.3.1 Exchange Statistics
      • 2.3.2 Fractional Quantum Hall Anyons
      • 2.3.3 Toric Code
  • Chapter 3: Path Integral
    • 3.1 Quantization
      • 3.1.1 Geometric Optics
      • 3.1.2 Physical Optics
      • 3.1.3 Particle-Wave Unification
    • 3.2 Propagator
      • 3.2.1 Path Integral Formulation
      • 3.2.2 Schrödinger Equation
      • 3.2.3 Free Particle Propagator
    • 3.3 Stationary Phase
      • 3.3.1 Stationary Phase Approximation
      • 3.3.2 WKB Approximation
      • 3.3.3 Bohr-Sommerfeld Quantization
    • 3.4 Imaginary Time
      • 3.4.1 Wick Rotation
      • 3.4.2 Statistical Mechanics
      • 3.4.3 Instantons
  • Chapter 4: Phase and Gauge
    • 4.1 Gauge Field
      • 4.1.1 Gauge Principle
      • 4.1.2 Electromagnetic Coupling
      • 4.1.3 Gauge Invariance
    • 4.2 Berry Phase
      • 4.2.1 Berry Phase
      • 4.2.2 Aharonov-Bohm Effect
      • 4.2.3 Flux Ring
    • 4.3 Landau Level
      • 4.3.1 Cyclotron Motion
      • 4.3.2 Landau Quantization
      • 4.3.3 Quantum Hall Effect
    • 4.4 Spin and Monopole
      • 4.4.1 Classical Spin
      • 4.4.2 Dirac Monopole
      • 4.4.3 Monopole Harmonics
  • Chapter 5: Perturbation Theory
    • 5.1 Time-Independent Perturbation Theory
      • 5.1.1 Toy Model
      • 5.1.2 Non-Degenerate Perturbation Theory
      • 5.1.3 Degenerate Perturbation Theory
    • 5.2 Time-Dependent Perturbation Theory
      • 5.2.1 Interaction Picture
      • 5.2.2 Fermi’s Golden Rule
      • 5.2.3 Applications
  • Chapter 6: Quantum Foundations
    • 6.1 Density Matrix
      • 6.1.1 Mixed States
      • 6.1.2 Entropy
      • 6.1.3 Quantum Statistics
    • 6.2 Entanglement
      • 6.2.1 Composite Systems
      • 6.2.2 Entanglement Measures
      • 6.2.3 Bell Inequality
    • 6.3 Generalized Measurement
      • 6.3.1 Projective Measurement
      • 6.3.2 POVM
      • 6.3.3 Quantum Channels
    • 6.4 Open Quantum Systems
      • 6.4.1 Decoherence
      • 6.4.2 Lindblad Master Equation
      • 6.4.3 Error Correction

Index

A | B | C | D | E | F | G | I | K | L | M | P | Q | S | U | V | W

A

  • Adiabatic theorem
  • Aharonov-Bohm effect
  • Angular momentum algebra
  • Anyons

B

  • Berry phase
  • Bloch sphere
  • Bohr-Sommerfeld quantization
  • Born rule
  • Bosons / Fermions

C

  • CHSH inequality
  • Covariant derivative

D

  • Degenerate perturbation
  • Density matrix
  • Dirac quantization

E

  • Entanglement

F

  • Fermi's golden rule
  • First-order energy
  • Free-particle propagator

G

  • Gauge transformation

I

  • Identical particles
  • Interaction picture

K

  • Ket notation |\psi\rangle

L

  • Landau levels
  • Lindblad equation

M

  • Minimal coupling

P

  • Partial trace
  • Partition function
  • Path integral
  • Pauli matrices
  • Perturbation series
  • POVM
  • Propagator

Q

  • Quantum channel
  • Qubit

S

  • Schrödinger equation
  • Second quantization
  • Second-order energy
  • Slater determinant
  • Stationary phase

U

  • Uncertainty principle

V

  • Von Neumann entropy

W

  • Wick rotation
  • WKB approximation

By Yi-Zhuang You

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Lecture notes prepared with Claude Code and Cursor AI.