Quantum mechanics


Ground state

Stationary state

Dirac bra-ket notation

Vector space

Vector space of functions

Inner product space

Vector subspace and eigenspace

Completeness of a vector space

Hilbert space

Kronecker product


Commuting operators

The uncertainty principle

Spectral decomposition of an operator

Matrix elements of an operator

Projection operator

Expectation value

Hermitian operator

Eigenfunctions and eigenvalue equations

Linear combination of wavefunctions

Postulates of quantum mechanics

One-particle, time-independent Schrodinger equation

One-particle, time-independent Schrodinger equation in spherical coordinates

1-D classical wave equation

One-particle, time-dependent Schrodinger equation

Classical angular momentum

Relation between magnetic dipole moment and angular momentum

Classical orbital angular momentum

Quantum orbital angular momentum operators (Cartesian coordinates)

Quantum orbital angular momentum operators (spherical coordinates)

Commutation relations of quantum orbital angular momentum operators

Quantum orbital angular momentum ladder operators

Eigenvalues of quantum orbital angular momentum operators

Matrix elements of angular momentum ladder operators

The vector model of quantum angular momentum

Larmor precession of an electron

Biot-Savart law

The Stern-Gerlach experiment

Gyromagnetic ratio of the electron

Spin angular momentum

Pauli matrices

Sequential Stern-Gerlach experiments

Composite systems

Composite systems – beyond spin operators

The singlet and triplet states

Quantum entanglement

Einstein-Podolsky-Rosen paradox

Bell’s inequality

Quantum key distribution

Light polarisation


Pockels cell

Photon polarisation

BB84 protocol

Exchange operator

Pauli exclusion principle

Non-relativistic multi-electron Hamiltonian

Exchange force

Many-electron systems

Time dilation

Length contraction

Thomas precession

Spin-orbit coupling

Perturbation theory

Degenerate perturbation theory

Degenerate perturbation theory (an example)

Time-dependent perturbation theory

Relativistic one-electron Hamiltonian

Relativistic many-electron Hamiltonian

Russell Saunders coupling

Term symbols

Constructing atomic terms (uncoupled representation)

Constructing atomic terms (coupled representation)

Hund’s rules

The variational method

Overlap integral

Central force problem

Reduction of the two-particle problem to one-particle problems

Rayleigh-Jeans law

Planck radiation law


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