Quantum mechanics

From Physics wiki

Introduction

• Prerequisites

Old quantum theory

Black-body radiation Photoelectric effect Compton effect Double-slit experiment Wave–particle duality de Broglie hypothesis

Many-slit diffraction Single-slit diffraction Stern-Gerlach experiment Bohr-Sommerfield model of the atom Bohr-Sommerfield-Wilson quantization condition

Matrix mechanics

Observable Measurement State Operator Density matrix Postulates

Position representation Momentum representation Canonical commutation relations Heisenberg uncertainty principle For reference: Bra-ket notation

Dynamics

• Schrödinger picture
• Schrödinger equation
• Poisson bracket
• Heisenberg picture
• Ehrenfest's theorem
• Liouville equation

Wave mechanics

Wavefunction Probability current Parity Wave packet One dimensional potentials Step potential

Square well potential Particle in a ring Delta function potential Harmonic oscillator Three dimensional potentials Particle in a box

Group theory and quantum mechanics

• Groups and representations
• Galilean group
• Rotation group

Angular momentum and spin

• Angular momentum
• Angular momentum and rotation
• Spherical harmonics
• Spin
• Angular momentum and parity
• Addition of angular momentum
• Clebsch-Gordan decomposition
• Bloch sphere
• Rotational coherent state
• Wigner-Eckart theorem

Central potential

• Spherical potential well
• 2D harmonic oscillator
• 3D harmonic oscillator
• Laplace-Runge-Lenz vector
• Rigid rotor
• Linear confining potential

Hydrogen atom

• Separation of variables
• Radial equation
• Kramers' relation
• Fine structure
• Hyperfine structure

Perturbation theory

• Time independent perturbation theory
• Degenerate perturbation theory
• Time dependent perturbation theory
• Harmonic perturbation
• Fermi's golden rule
• Brillouin-Wigner perturbation theory
• Strong-coupling expansion
• Anharmonic oscillator

Interaction with an electromagnetic field

• Coupling to an electromagnetic field
• Charged particle in a static, homogeneous magnetic field field (Landau levels)
• Kramers' theorem
• Zeeman effect
• Paschen-Back effect
• Stark effect
• Magnetic resonance
• Absorption and stimulated emission
• Electric dipole approximation

See also: Quantum optics (subject)

Bound states

Scattering

• Scattering amplitude
• Cross section
• Lippmann-Schwinger equation
• Born approximation
• Partial wave expansion
• Optical theorem
• Scattering off of a hard sphere
• Scattering off of a Yukawa potential
• Rutherford scattering
• Scattering form factor
• Resonance
• Breit-Wigner formula
• Eikonal approximation

Approximation

• WKB approximation
• Variational principle (Rayleigh-Ritz approximation)
• Adiabatic approximation
• Bethe ansatz
• Feynman-Hellmann theorem

Selection rules and sum rules

• Thomas-Reiche-Kuhn sum rule
• Superselection

Non-perturbative effects

• Instanton

Many particle systems

• Spin and statistics
• Pauli exclusion principle
• H₂⁺ ion
• H₂ molecule
• Helium atom
• Born-Oppenheimer approximation
• Aufbau principle
• Multiparticle state
• Fock space
• Second quantization
• Møller-Plesset perturbation theory
• Density functional theory

Quantized electromagnetic field

• Quantization of the electromagnetic field

See also: Quantum optics (subject)

Advanced

• Geometric phase (Berry's phase)
• Aharonov-Bohm effect
• Entanglement
• Bell's theorem
• No cloning theorem
• Teleportation
• Coherent state
• Classical limit

Path integral formulation

• Path integral
• Duru-Kleinert transformation

Relativistic quantum mechanics

• Klein-Gordon equation
• Scalar particle in a Coulomb potential
• Dirac equation
• Pauli equation
• Dirac particle in a Coulomb potential
• Klein paradox

Open and dissipative systems

• Open system
• Decoherence
• Einselection
• Irreversible relaxation
• Bipartite system

See also: open quantum systems (Statistical mechanics)

Other topics

Quantum recurrence theorem Hanbury Brown-Twiss effect Stone–von Neumann theorem (the "choice problem") Kochen-Specker theorem Pauli's theorem

Weak measurement Lagrangian formulation Bethe Ansatz Gutzwiller trace formula Pedagogical models

See also: Quantum cryptography (Quantum information)

Quantum information

See: Quantum information (subject)

Resources

• Books
• Websites
• Lectures

Appendix

• Notation and conventions