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Quantum mechanics plays a central role in our understanding of fundamental phenomena, primarily in the microscopic domain. It lays the foundation for an understanding of atomic, molecular, condensed matter, nuclear and particle physics.
Topics covered include:
- the basic principles of quantum mechanics (probability interpretation; Schrödinger equation; Hermitian operators, eigenstates and observables; symmetrisation, antisymmetrisation and the Pauli exclusion principle; entanglement)
- wave packets, Fourier transforms and momentum space
- eigenvalue spectra and delta-function normalisation
- Heisenberg uncertainty principle
- matrix theory of spin
- the Hilbert space or state vector formation using Dirac bra-ket notation
- the harmonic oscillator
- the quantisation of angular momentum and the central force problem including the hydrogen atom
- approximation techniques including perturbation theory and the variational method
- applications to atomic and other systems.
Intended learning outcomes
Students completing this subject should be able to:
- explain the basic principles of quantum physics including the probability interpretation, unitary time-evolution, the association of operators with observables, Pauli exclusion principle, and entanglement;
- solve elementary problems involving intrinsic spin;
- solve problems by applying quantum mechanical theory to situations involving atoms, molecules, solids, nuclei and elementary particles;
- appreciate the importance of approximation techniques in quantum mechanics.
A student who completes this subject should be able to:
- analyse how to solve a problem by applying simple fundamental laws to more complicated situations
- apply abstract concepts to real-world situations
- solve relatively complicated problems using approximations
- participate as an effective member of a group in tutorial discussions
- manage time effectively in order to be prepared for tutorial classes, undertake the written assignments and the examination.
Last updated: 8 August 2023