Outline

Overview

Quantum statistical physics has revolutionized the world we live in - providing a profound understanding of the microscopic world and driving the technological revolution of the last few decades. Modern physics increasingly relies on solving equations using computational techniques, for modelling anything from the big bang to quantum dot lasers. The advanced unit covers the same overall concepts as PHYS3034 but with a greater level of challenge and academic rigour, largely in separate lectures. You will study techniques of quantum mechanics to predict the energy-level structure of electrons in atoms, introducing techniques useful in the broad field of quantum physics, with applications e. g. in atomic clocks. You will study the theoretical foundation of statistical mechanics, including both classical and quantum distributions. You will apply a variety of numerical schemes for solving ordinary and partial differential equations, learn about the suitability of particular methods to particular problems, and their accuracy and stability. The module includes computational lab sessions, in which you will actively solve a range of physics problems. In completing this unit you will gain understanding of the foundations of modern physics and develop skills that will enable you to numerically solve complex problems in physics and beyond.

Unit details and rules

Academic unit	Physics Academic Operations
Credit points	6
Prerequisites ?	Average of 70 or above in [(PHYS2011 OR PHYS2911 OR PHYS2921) AND (PHYS2012 OR PHYS2912 OR PHYS2922)]
Corequisites ?	None
Prohibitions ?	PHYS3034 or PHYS3039 or PHYS3939 or PHYS3042 or PHYS3942 or PHYS3043 or PHYS3943 or PHYS3044 or PHYS3944 or PHYS3090 or PHYS3990 or PHYS3991 or PHYS3999 or PHYS3099
Assumed knowledge ?	(MATH2021 OR MATH2921 OR MATH2061 OR MATH2961 OR MATH2067)
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Jonathan Bland-Hawthorn, jonathan.bland-hawthorn@sydney.edu.au
Lecturer(s)	Ben Fulcher, ben.fulcher@sydney.edu.au
	Andrew Doherty (Physics), andrew.doherty@sydney.edu.au
	Stephen Bartlett, stephen.bartlett@sydney.edu.au

Type	Description	Weight	Due	Length
Final exam (Take-home short release)	Final exam Take home, open book, 3-hour, time-limited exam, 15 min extra to upload.	50%	Formal exam period	3 hours
Outcomes assessed:
Online task	Quantum physics quiz Canvas quiz in weeks 7, 8, 10, 12	8%	Multiple weeks	15 minutes
Outcomes assessed:
Skills-based evaluation	Computational Physics Computer Labs Weeks 7, 8, 9, 10, 11, 12, 13; see Canvas for details.	14%	Multiple weeks	2 hours
Outcomes assessed:
Online task	Statistical mechanics quiz Canvas quiz	3%	Week 04	15 minutes
Outcomes assessed:
Assignment	Statistical mechanics assignment Written assessment	5%	Week 06 Due date: 31 Mar 2022 at 23:59	~ 5 pages
Outcomes assessed:
Assignment	Problem assignment Written assessment	10%	Week 08 Due date: 14 Apr 2022 at 23:59	~ 10 pages
Outcomes assessed:
Assignment	Computational physics assignment Written assessment	5%	Week 12 Due date: 20 May 2022 at 23:59	~ 5 pages
Outcomes assessed:
Assignment	Quantum physics assignment Written assessment	5%	Week 13 Due date: 27 May 2022 at 23:59	~ 5 pages
Outcomes assessed:
= Type D final exam ?

Assessment summary

Assignments: There are four assignments in this unit, one per module and one larger problem assignment using aspects of both, quantum and statistical physics. You are encouraged to start early on the problem assignment as you will be able to solve aspects from it as early as it is released. Assignments are to be submitted through Canvas. Typewritten and handwritten assignments are acceptable – for handwritten assignment make sure the scans have good resolution and contrast and are not blurry or distorted. Only parts of the assignment that can readily be read on screen will be marked. Plan plenty of time for uploading your files ahead of the deadline to make room for connectivity issues, as deadlines will be enforced strictly. It is your responsibility to ensure that files have uploaded correctly with all pages.
Quizzes: There will be one statistical mechanics quiz, and 4 quantum physics quizzes. All quizzes will be online and last 15 minutes. You will have to do each quiz within a 24h window on the due date.
Computational Physics Computer Labs: The laboratory sessions consist of sets of exercises requiring you to modify the codes introduced in the lectures (available via the Canvas site), and to write your own codes. The tasks involve implementing numerical methods and solving science problems. The laboratory sessions support the lecture material, and are a crucial part of the unit. The lab question sheets are available online as a Canvas quiz, and you may complete the lab at any time each week before the due date. Tutors will be available during the scheduled computer labs to assist you.
Final exam: The final exam will have questions covering all three aspects of this course. This will be a take home, open book, 3-hour, time-limited exam, 15 min extra to upload.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name	Mark range	Description
High distinction	85 - 100	A student demonstrates a flair for the subject and comprehensive knowledge and understanding of the unit material. A ‘High Distinction’ reflects exceptional achievement and is awarded to a student who demonstrates the ability to apply subject knowledge to novel situations.
Distinction	75 - 84	A student demonstrates an aptitude for the subject and a solid knowledge and understanding of the unit material. A ‘Distinction’ reflects excellent achievement and is awarded to a student who demonstrates an ability to apply the key ideas of the subject.
Credit	65 - 74	a student demonstrates a good command and knowledge of the unit material. A ‘Credit’ reflects solid achievement and is awarded to a student who has a broad understanding of the unit material but has not fully developed the ability to apply the key ideas of the subject.
Pass	50 - 64	At PS level, a student demonstrates proficiency in the unit material. A ‘Pass’ reflects satisfactory achievement and is awarded to a student who has threshold knowledge of the subject.
Fail	0 - 49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Weekly schedule

WK	Topic	Learning activity
Week 01	Statistical Physics Lectures: Introduction, Boltzmann Distribution; Partition Function; Ideal Gas	Lecture (3 hr)
Week 01	Statistical Physics Computer Lab 1: Paramagnetism, Einstein Solid	Computer laboratory (2 hr)
Week 02	Statistical Physics Lecture: Quantum Statistics; Bosons and Fermions	Lecture (1 hr)
	Statistical Physics Tutorial	Tutorial (1 hr)
	Statistical Physics Computer Lab 2: Maxwell speed distribution, Blackbody radiation	Computer laboratory (2 hr)
	Complex Linear Algebra for Quantum Physics 1	Tutorial (1 hr)
Week 03	Statistical Physics Lectures: Degenerate Fermi gas at zero temperature; Black holes & Hawking radiation; Density of States	Lecture (3 hr)
	Statistical Physics Tutorial	Tutorial (1 hr)
	Statistical Physics Computer Lab 3: Einstein vs Debye, ferromagnetism	Computer laboratory (2 hr)
	Complex Linear Algebra for Quantum Physics 2	Tutorial (1 hr)
Week 04	Statistical Physics Lectures: Ising model of a ferromagnet	Lecture (1 hr)
	Quantum Physics Lectures: Review of Dirac notation and state-space. Operators in quantum mechanics; Commutation Relations; Time evolution and the Schroedinger equation. The Hamiltonian as the generator of time translations. Wavefunctions in infinite-dimensional Hilbert spaces; Position and Momentum Operators;	Lecture (2 hr)
	Statistical Physics Tutorial	Tutorial (1 hr)
	Statistical Physics Computer Lab 4: QUIZ+Ising model, Metropolis Monte Carlo	Computer laboratory (2 hr)
Week 05	Statistical Physics Lecture: Statistical mechanics of error correction and the toric code	Lecture (1 hr)
	Quantum Physics Lectures: Uncertainty relations; Time-independent Schroedinger equation; Particle in a box; Introduction to wave mechanics in 3D; The generator of rotations; Angular momentum	Lecture (2 hr)
	Quantum Physics Tutorial	Tutorial (1 hr)
	Statistical Physics Computer Lab 5: Wolff sampling, critical slowdown	Computer laboratory (2 hr)
Week 06	Statistical Physics Lecture: Bose-Einstein condensation	Lecture (1 hr)
	Statistical Physics Tutorial	Tutorial (1 hr)
	Statistical Physics Computer Lab 6: Continuous phase transitions, critical phenomena, RG	Computer laboratory (2 hr)
	Quantum Physics Lectures: Angular momentum eigenstates; Ladder operators; Spin-1/2 systems; Angular momentum in a 3D spherical system	Lecture (2 hr)
Week 07	Quantum Physics Lectures: Solving the Schroedinger Equation in a 3D radially symmetric potential; The spherical harmonics; Intrinsic vs orbital angular momentum	Lecture (2 hr)
	Quantum Physics Tutorial	Tutorial (1 hr)
	Computational Physics Lecture 1: Types of numerical error – rounding and range error, truncation error; Euler's method	Lecture (1 hr)
	Computational Physics Computer Lab 1: Types of numerical error – rounding and range error, truncation error; Euler's method	Computer laboratory (2 hr)
Week 08	Quantum Physics Lectures:The Hydrogen atom; Radial wavefunctions; Hydrogenic wavefunctions; Hydrogen spectroscopy; Hydrogen Spectroscopy; Selection Rules; Multielectron Atoms; Spectroscopic Notation	Lecture (2 hr)
	Quantum Physics Tutorial	Tutorial (1 hr)
	Computational Physics Lecture 2: Dynamical ODEs – the Kepler problem; Non-dimensionalisation of the problem; The Verlet method; Properties of the Verlet method	Lecture (1 hr)
	Computational Physics Computer Lab 2: Dynamical ODEs – the Kepler problem; Non-dimensionalisation of the problem; The Verlet method; Properties of the Verlet method	Computer laboratory (2 hr)
Week 09	Quantum Physics Lectures: Nondegenerate Perturbation Theory; Degenerate perturbation theory; spin-orbit coupling; Fine structure	Lecture (2 hr)
	Quantum Physics Tutorial	Tutorial (1 hr)
	Computational Physics Lecture 3: General form of ODEs for numerical solution; Runge-Kutta (Taylor series) methods; Fourth order Runge-Kutta (RK4); Deriving second order Runge-Kutta (RK2)	Tutorial (1 hr)
	Computational Physics Computer Lab 3: General form of ODEs for numerical solution; Runge-Kutta (Taylor series) methods; Fourth order Runge-Kutta (RK4); Deriving second order Runge-Kutta (RK2)	Computer laboratory (2 hr)
Week 10	Quantum Physics Lectures: Addition of angular momentum; Hyperfine structure; Generalized Clebsch-Gordan coefficients ; Atoms in static fields; The Stark Effect; The Zeeman effect; The Hamiltonian for classical fields; Charged particle in an EM field; Radiation	Lecture (2 hr)
	Quantum Physics Tutorial	Tutorial (1 hr)
	Computational Physics Lecture 4: Partial Differential Equations or PDEs; Classification of PDEs (Initial Value Problems or IVPs and BVPs); Parabolic PDEs and the diffusion equation; Forward-Time Centred Space discretisation, and solution for diffusion, numerical stability of FTCS for 1-D diffusion	Lecture (1 hr)
	Computational Physics Computer Lab 4: Partial Differential Equations or PDEs; Classification of PDEs (Initial Value Problems or IVPs and BVPs); Parabolic PDEs and the diffusion equation; Forward-Time Centred Space discretisation, and solution for diffusion, numerical stability of FTCS for 1-D diffusion	Computer laboratory (2 hr)
Week 11	Quantum Physics Lectures: Time-dependent perturbation theory; The interaction picture; Fermi’s golden rule	Lecture (2 hr)
	Quantum Physics Tutorial	Tutorial (1 hr)
	Computational Physics Lecture 5: Hyperbolic PDEs and the wave and advection equations; FTCS applied to advection; von Neumann stability analysis; Lax method for advection	Lecture (1 hr)
	Computational Physics Computer Lab 5: Hyperbolic PDEs and the wave and advection equations; FTCS applied to advection; von Neumann stability analysis; Lax method for advection	Computer laboratory (2 hr)
Week 12	Quantum Physics Lectures: Electric dipole approximation; Selection Rules; Spontaneous and Stimulated; Laser-driven transitions; the density matrix	Computer laboratory (2 hr)
	Quantum Physics Tutorial	Tutorial (1 hr)
	Computational Physics Lecture 6 : 2-D elliptic PDEs and the Laplace and Poisson equations; Jacobi and Gauss-Seidel methods of relaxation for elliptic PDEs; Successive Over-Relaxation or SOR for elliptic PPDs;	Lecture (1 hr)
	Computational Physics Computer Lab 6 : 2-D elliptic PDEs and the Laplace and Poisson equations; Jacobi and Gauss-Seidel methods of relaxation for elliptic PDEs; Successive Over-Relaxation or SOR for elliptic PPDs;	Computer laboratory (2 hr)
Week 13	Quantum Physics Lectures: optical Bloch equations; Optical forces on atoms and laser cooling of atoms – non examinable;	Lecture (2 hr)
	Quantum Physics Tutorial	Lecture (1 hr)
	Computational Physics Lecture 7 : Order/accuracy of PDE solution methods; Implicit methods for diffusion (Crank-Nicolson); More general diffusion problems; Summary and recap	Lecture (1 hr)
	Computational Physics Computer Lab 7 : Order/accuracy of PDE solution methods; Implicit methods for diffusion (Crank-Nicolson); More general diffusion problems; Summary and recap	Computer laboratory (2 hr)

Attendance and class requirements

There will be no practicals – only computer labs, which are well suited for online delivery. Students will now have a week to complete the computer labs. Instead of checkpoints students will fill out a canvas quiz (not timed).

Tutors will be available to help them during the scheduled computer lab hours (2 hours weekly).

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

All readings for this unit can be accessed on the Library eReserve link available in the Canvas site for this unit.

John Townsend, “A Modern Approach to Quantum Mechanics”, University Science Books
McIntyre, D.H., Minogue, C.A., Tate, J., "Quantum Mechanics," Pearson
Schroeder, Daniel V., “An introduction to thermal physics,” Addison Wesley
Garcia, A., "Numerical methods for physics" (any edition)
Press, W.H. et al. "Numerical Recipes" (any edition)

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. demonstrate an understanding of key concepts in two foundation areas of physics – quantum mechanics of atoms and statistical physics
LO2. apply these concepts to develop models, and to solve qualitative and quantitative problems in scientific contexts, using appropriate mathematical and computing techniques as necessary – Compare and critique different models in quantum and statistical physics
LO3. design computer programs to solve physical problems
LO4. compare and critique different approaches to numerically solving physical problems
LO5. communicate scientific information appropriately, through written work
LO6. analyse a physical problem in quantum physics and statistical physics and develop a formalism appropriate for solving it
LO7. demonstrate a sense of responsibility, ethical behaviour, and independence as a learner and as a scientist.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

No changes have been made since this unit was last offered.

Additional information

The School of Physics recognises that biases and discrimination, including but not limited to those based on gender, race, sexual orientation, gender identity, religion and age, continue to impact parts of our community disproportionately. Consequently, the School is strongly committed to taking effective steps to make our environment supportive and inclusive and one that provides equity of access and opportunity for everyone.

The School has three Equity Officers as a point of contact for students and staff who may have a query or concern about any issues relating to equity, access and diversity. If you feel you have been treated unfairly, bullied, discriminated against or disadvantaged in any way, you are encouraged to talk to one of the Equity Officers or any member of the Physics staff.

More information can be found at https://sydney.edu.au/science/schools/school-of-physics/equity-access-diversity.html

Any student who feels they may need a special accommodation based on the impact of a disability should contact Disability Services:

http://sydney.edu.au/current_students/disability/ who can help arrange support.

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

No eating or drinking is allowed in any laboratory under any circumstances
A laboratory coat and closed-toe shoes are mandatory
Follow safety instructions in your manual and posted in laboratories
In case of fire, follow instructions posted outside the laboratory door
First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

PHYS3934: Quantum, Statistical and Comp Phys (Adv)

Semester 1, 2022 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect