Formalism of Quantum Mechanics
i. Formalism of Quantum Mechanics as a Linear Theory: probability interpretation of the wave function Y, normalisation;
ii. Linear superposition, overlap integrals, vector interpretation and Dirac notation;
iii. Observables and operators, measurements;
iv. Eigenfunctions, eigenvalues, Hermitian operators, properties of eigenfunctions and eigenvalues of Hermitian operators;
v. Expectation values;
vi. Eigenfunction expansions and analogy with Fourier series, momentum eigenfunctions, orthogonality and completeness, physical meaning of expansion coefficients, commuting and compatible observables, Heisenberg's Uncertainty Principle;
vii. The timedependent Schrödinger equation.
Angular Momentum and Spin
i. Angular momentum operators and commutation relations;
ii. Angular momentum eigenfunctions and eigenvalues, the magnetic and orbital angular momentum quantum numbers, spherical harmonics;
iii. Matrix representation of operators, ladder operators;
iv. Intrinsic spin, total angular momentum, addition of spin;
v. The SternGerlach experiment
The Hydrogenic Atom
i. Energy eigenfunctions for the hydrogenic atom;
ii. Energy levels and quantum numbers, Pauli Exclusion Principle and general properties of hydrogenic atoms including orbital shapes and form of radial distribution function.
Approximation Methods
i. Variational method and application to the simple harmonic oscillator;
ii. Nondegenerate timeindependent perturbation theory, firstorder correction to the energy, firstorder correction to the eigenfunctions and secondorder correction to the energy;
iii. Application to the hydrogen atom (gravitational effects, Zeeman effect, spinorbit coupling and other perturbations);
