Quantum mechanics
Vector subspace and eigenspace
Completeness of a vector space
Spectral decomposition of an operator
Matrix elements of an 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
One-particle, time-dependent Schrodinger equation
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
Gyromagnetic ratio of the electron
Sequential Stern-Gerlach experiments
Composite systems – beyond spin operators
The singlet and triplet states
Einstein-Podolsky-Rosen paradox
Non-relativistic multi-electron Hamiltonian
Degenerate perturbation theory
Degenerate perturbation theory (an example)
Time-dependent perturbation theory
Relativistic one-electron Hamiltonian
Relativistic many-electron Hamiltonian
Constructing atomic terms (uncoupled representation)
Constructing atomic terms (coupled representation)
Reduction of the two-particle problem to one-particle problems
Binomial theorem and binomial series
Generating function for the Legendre polynomials
Recurrence relations of the Legendre polynomials
Rodrigues’ formula of the Legendre polynomials
Orthogonality of the Legendre polynomials
Normalisation constant of the Legendre polynomials
Associated Legendre polynomials
Generating function for the associated Legendre polynomials
Recurrence relations of the associated Legendre polynomials
Orthogonality of the associated Legendre polynomials
Normalisation constant of the associated Legendre polynomials
Orthogonality of the spherical harmonics
Normalisation constant of the spherical harmonics
Rodrigues’ formula for the Laguerre polynomials
Generating function for the Laguerre polynomials
Recurrence relations of the Laguerre polynomials
Orthogonality of the Laguerre polynomials
Associated Laguerre polynomials
Rodrigues’ formula for the associated Laguerre polynomials
Generating function for the associated Laguerre polynomials
Recurrence relations of the associated Laguerre polynomials
Orthogonality of the associated Laguerre polynomials
Normalisation constant of the associated Laguerre polynomials
Total wavefunction of a hydrogenic atom
Degeneracy in hydrogenic atoms