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Course profile

Statistical Mechanics (PHYS3020)

Study period
Sem 2 2024
Location
St Lucia
Attendance mode
In Person

Course overview

Study period
Semester 2, 2024 (22/07/2024 - 18/11/2024)
Study level
Undergraduate
Location
St Lucia
Attendance mode
In Person
Units
2
Administrative campus
St Lucia
Coordinating unit
Mathematics & Physics School

Theoretical understanding of the physical properties of samples of material of macroscopic size, on the basis of the known quantum mechanical behaviour of the constituent (microscopic) particles; micro-canonical, canonical, and grand-canonical ensembles; classical and quantum gases; photons and phonons; Planck distribution and black-body radiation; fermions and bosons; Fermi-Dirac distribution and Fermi energy; Bose-Einstein distribution and Bose condensation.

The course will cover the microscopic (Statistical Mechanics) approaches to thermal physics, including: micro-canonical, canonical, and grand-canonical ensembles; classical and quantum gases; photons and phonons; Planck distribution and black-body radiation; fermions and bosons; Fermi-Dirac distribution and Fermi energy; Bose-Einstein distribution and Bose condensation.

Statistical mechanics is the incredibly successful theory which allows us to describe macroscopic or thermodynamic properties of materials in terms of the known dynamics (either classical or quantum) of the constituent microscopic particles (such as atoms and molecules). Statistical mechanics gives a microscopic understanding of phenomena as diverse as entropy and the second law of thermodynamics, the ideal gas law, the cosmic microwave background radiation, neutron stars, superfluidity, the denaturation of proteins, carbon monoxide poisoning, magnetic phase transitions, and the electronic properties of metals. These diverse applications will be illustrated in the tutorial problems.

The subject provides part of a comprehensive, complete and coherent program of education in Physics intended for students aiming to become professional physicists. It is a compulsory subject for entry into Physics Postgraduate Honours.

The course would also be beneficial to students in biochemistry, chemistry, computer science, materials science, and mechanical and chemical engineering.

Course requirements

Assumed background

Essential:

MATH2000/2001/2901 – Calculus and Linear Algebra II

PHYS2020 – Thermodynamics and Condensed Matter Physics

PHYS2041 – Quantum Physics

Desirable:

MATH2100 –ᅠApplied Mathematical Analysis

PHYS3040 –ᅠQuantum Physics

Intending students need to be competent in calculus, particularly including the theory of first order partial derivatives. The course is presented on the assumption that the student is familiar with second year Thermodynamics as outlined, for example, in the textbook by Herbert Callen or in the first few chapters of Daniel Schroeder's "Thermal Physics" and covered in PHYS2020ᅠThe development proceeds from an assumed background that includes all the basic results of a course in elementary quantum mechanics such as PHYS2041. A knowledge of basic statistics and probability theory is also desirable.ᅠ

More specifically, the expected capabilities on entering the course are as follows:

In addition to the general first year capabilities, such as

  • basic differentiation and integration
  • finding extrema of a function
  • integration as area under a curve
  • visualise and sketch simple functions
  • visualise a function of 2 variables (eg contour plot)
  • logarithms, exponentials and trigonometric functions
  • definite vs indefinite integrals
  • Taylor series of elementary functions, especially of exp(x) and ln(1+x).
  • conversion between commonly used units
  • keeping track of units in a calculation
  • using simple checks to assess whether an answer makes sense (e.g. dimensions, orders-of-magnitude, limiting behaviours, consistency with fundamental principles and axioms)

students are expected to have the following core skills from 2nd year physics and mathematics courses:

1. Conceptual understanding

From second-year thermodynamics (PHYS2020):

  • basic understanding of temperature, entropy, heat versus work, heat capacity
  • familiarity with the laws of thermodynamics and the ideal gas law
  • practical application of partial derivatives, for e.g. calculating the heat capacity of various physical systems

From second-year quantum (PHYS2040):

Statistical mechanics makes use of a variety of results from quantum mechanics. Students should have basic knowledge or familiarity with:

  • the quantum mechanical wavefunction
  • quantum numbers and energy levels for a particle in a rectangular potential well (finite box potential) and a particle in a harmonic potential (harmonic oscillator problem); familiarity with the respective quantum wavefunctions
  • quantum mechanics of angular momentum and addition of angular momenta;
  • concept of spin;
  • wave optics, characteristics of light – wavelengths/frequency
  • photons and the ideas behind quantisation of electromagnetic field;
  • quantised energy levels of a mode of electromagnetic field;
  • black-body radiation.

Although they are covered in the course, it would be an advantage for students to be familiar with basic ideas behind quantum mechanical treatment of systems of identical particles:

  • symmetric versus anti-symmetric wavefunctions;
  • fermions and bosons;
  • Pauli exclusion principle.

2. Mathematics skills

  • Knowledge, understanding, and manipulation of elementary functions such as powers, exponentials, logarithms (including manipulations involving log(AB) and log(A/B)), trigonometric functions, as well functions of complex variables such as exp(ix), and hyperbolic functions (sinh(x), cosh(x), tanh(x) etc.);
  • Differentiation: practical knowledge of derivatives of elementary functions, application of the chain rule, and knowledge of partial derivatives;
  • Integration: distinction between definite and indefinite integrals, integrals of elementary functions, integration by parts; understanding of line, surface, volume, and multiple integrals;
  • Even and odd functions, integrals of even and odd functions between symmetric boundaries;
  • Gaussian function – mathematical form and properties; ability to evaluate the mean and the dispersion of a Gaussian, ability to illustrate these quantities graphically;
  • Elementary vector algebra; addition of vectors, evaluation of their length;
  • Basic knowledge of the theory of probabilities, statistics, and combinatorics; understanding of permutations, factorials, binomial coefficients etc.;
  • Knowledge of the geometric series and binomial expansion.

3. Experimental

  • design and conduct simple measurements using electrical multimeters, oscilloscopes, thermometers, rulers, etc.;
  • estimate uncertainties and propagate uncertainties through calculations;
  • write a structured laboratory report, including literature exploration and appropriate citation.

Prerequisites

You'll need to complete the following courses before enrolling in this one:

PHYS2020 + [MATH2000 or MATH2001] + PHYS2041

Recommended prerequisites

We recommend completing the following courses before enrolling in this one:

MATH2100

Incompatible

You can't enrol in this course if you've already completed the following:

PHYS3920 and PHYS7021 (co-taught)

Jointly taught details

This course is jointly-taught with:

PHYS3020, PHYS3920 and PHYS7021 are co-badged courses and will share learning activities and assessment. Lectures and laboratories are the same, a separate tutorial section (covering the same content) is available for Advanced Science students.

Course contact

Course staff

Lecturer

Tutor

Mr Kyle Clunies-Ross
Ms Lauren McQueen
Mr Andoni Skoufris
Mr Jayden Hasted
Ms Divita Gautam
Miss Tavshabad Kaur
Mr David Sommers

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

Wednesday 14 August: Ekka show day - No lecture. No tutorial in week 4.

All classes will be conducted on campus. Consult your personal timetable for times and locations. Students are expected to attend these sessions in person unless they have a valid reason for being unable to attend (such as illness).

Important: if you are ill, then do not attend any classes in person. Alternative arrangements can be organised – consult Blackboard for details.