Major

# Mathematical Physics

### Navigation

## What will I study?

### Overview

You will gain a deep understanding of the physical world and develop skills in mathematical modelling, problem solving and critical thinking.

#### Your major structure

You’ll complete this major as part of a Bachelor of Science degree.

In your **first** and **second** **years** you will complete subjects that are prerequisites for your major, including mathematics and physics subjects.

In your **third year,** you will complete 50 points (four subjects) of deep and specialised study in mathematical physics.

Throughout your degree you will also take science **elective** subjects and **breadth** (non-science) subjects, in addition to your major subjects and prerequisites.

Read more about studying mathematics and physics at the University of Melbourne.

### Sample course plan

View some sample course plans to help you select subjects that will meet the requirements for this major.

These sample study plans assume that students have undertaken VCE Units 3/4 Physics and a study score of at least 29 in VCE Specialist Mathematics 3/4, or equivalent. If students have not completed this previously, they may first need to enrol in PHYC10009 Foundations of Physics and/or MAST10005 Calculus 1 in their first semester

Year 1

100 pts

- Semester 1 50 pts

- Semester 2 50 pts

Year 2

100 pts

- Semester 1 50 pts

- Semester 2 50 pts

Year 3

100 pts

- Semester 1 50 pts

- Semester 2 50 pts

These sample study plans assume that students have undertaken VCE Units 3/4 Physics and a study score of at least 29 in VCE Specialist Mathematics 3/4, or equivalent. If students have not completed this previously, they may first need to enrol in PHYC10009 Foundations of Physics and/or MAST10005 Calculus 1 in their first semester

Year 1

100 pts

- Semester 2 50 pts

- Summer term 12.5 pts

- Semester 1 37.5 pts

Year 2

100 pts

- Semester 2 50 pts
science elective

12.5 pts

science elective

12.5 pts

breadth

12.5 pts

- Semester 1 50 pts

Year 3

100 pts

- Semester 2 50 pts

- Semester 1 50 pts

### Explore this major

Explore the subjects you could choose as part of this major.

- 12.5 pts
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.

- 12.5 pts
Complex analysis is a core subject in pure and applied mathematics, as well as the physical and engineering sciences. While it is true that physical phenomena are given in terms of real numbers and real variables, it is often too difficult and sometimes not possible, to solve the algebraic and differential equations used to model these phenomena without introducing complex numbers and complex variables and applying the powerful techniques of complex analysis.

Topics include:the topology of the complex plane; convergence of complex sequences and series; holomorphic functions, the Cauchy-Riemann equations, harmonic functions and applications; contour integrals and the Cauchy Integral Theorem; singularities, Laurent series, the Residue Theorem, evaluation of integrals using contour integration, conformal mapping; and aspects of the gamma function.

#### Electives A

Complete one of the following subjects:

- Statistical Physics 12.5 pts
Statistical mechanics, the microscopic basis of classical thermodynamics, is developed in this subject. It is one of the core areas of physics, finding wide application in solid state physics, astrophysics, plasma physics and cosmology.

Using fundamental ideas from quantum physics, a systematic treatment of statistical mechanics is developed for systems in equilibrium. The content of this subject includes ensembles and the basic postulate; the statistical basis of the second and third laws of thermodynamics; canonical, micro-canonical and grand-canonical ensembles and associated statistical and thermodynamic functions; ideal quantum gases; black body radiation; the classical limit and an introduction to real gases and applications to solid state physics.

- Electrodynamics 12.5 pts
This subject provides an introduction to electrodynamics and a wide range of applications including communications, superconductors, plasmas, novel materials, photonics and astrophysics. Topics include: revision of Maxwell’s equations, strategies for solving boundary value problems for static and time-varying fields, electromagnetic fields in materials (including dielectrics, magnetic materials, conductors, plasmas and metamaterials), electromagnetic waves, derivation of geometric optics from Maxwell’s equations, guided waves, relativistic electrodynamics and the covariant formulation of electrodynamics, radiation by antennas and accelerating charged particles.

#### Electives B

Complete one of the following subjects:

- Metric and Hilbert Spaces 12.5 pts
This subject provides a basis for further studies in modern analysis, geometry, topology, differential equations and quantum mechanics.It introduces the idea of a metric space with a general distance function, and the resulting concepts of convergence, continuity, completeness, compactness and connectedness. The subject also introduces Hilbert spaces: infinite dimensional vector spaces (typically function spaces) equipped with an inner product that allows geometric ideas to be used to study these spaces and linear maps between them.

Topics include: metric and normed spaces, limits of sequences, open and closed sets, continuity, topological properties, compactness, connectedness; Cauchy sequences, completeness, contraction mapping theorem; Hilbert spaces, orthonormal systems, bounded linear operators and functionals, applications.

- Methods of Mathematical Physics 12.5 pts
This subject gives an example-oriented overview of various advanced topics that are important for mathematical physics and physics students, as well as being of interest to students of pure and applied mathematics. These topics include:

- Further differential equations: Bessel functions, Legendre polynomials, spherical harmonics and applications such as the Laplace/Schrodinger equation in polar/spherical coordinates;
- Further vector calculus: Differential forms, integration, Stokes’ theorem and applications such as Maxwell’s equations, charge conservation and Dirac monopoles;
- Hilbert spaces: L2 spaces, bounded and unbounded operators, normalisable and non-normalisable eigenfunctions, distributions and applications to quantum theory;
- Group theory: Lie groups and algebras, representations and applications such as quantum spin and particle physics.