68413 Quantum Physics
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Credit points: 6 cp
Result type: Grade and marks
Requisite(s): (68201 Physics 2 OR 68037 Physical Modelling) AND (33230c Mathematics 2 OR 68038 Advanced Mathematics and Physics OR 33290 Statistics and Mathematics for Science)
The lower case 'c' after the subject code indicates that the subject is a corequisite. See definitions for details.
These requisites may not apply to students in certain courses. See access conditions.
Recommended studies: some knowledge of complex numbers, matrices and differential equations
Description
This subject builds on introductory material on waves and classical mechanics. The subject examines how the behaviour of our world at an atomic level differs from our everyday experience of the macroscopic world. It introduces concepts and quantum mechanical tools needed to describe the structure and interactions of atoms, molecules and solids. The unique properties of matter at this scale can be exploited in the creation of new materials and devices in nanotechnology. This subject explores emerging technologies such as quantum computing, scanning tunelling microscopy, and spectroscopic tools used to characterise and investigate the atomic world. It provides material which is fundamental to understanding many areas of physics and chemistry together with contemporary applications which are relevant to nanotechnologists.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Evaluate how quantum-mechanical systems, states and observables are represented by mathematical entities and analyse the measurement process and the time-evolution of states. |
|---|---|
| 2. | Solve the Schrödinger equation for common one-dimensional situations e.g. the quantum well, the tunnel barrier and the harmonic oscillator. |
| 3. | Apply the most common quantum-mechanical operators, especially the Hamiltonian, the position, momentum, angular momentum and the ladder operators. |
| 4. | Calculate and apply the stationary states and energies of the unperturbed hydrogen atom. |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate coherent understanding of physics and related knowledge applied to diverse contexts. (1.1)
- Evaluate the reliability of scientific evidence and apply effective experimental design, analysis and critical thinking to predict the behaviour of real-world systems using physical models (2.1)
- Apply effective and appropriate communication methods for discussing physics concepts, data and analysis with diverse audiences. (5.1)
Contribution to the development of graduate attributes
GA1. Disciplinary knowledge
In the lectures, you will learn the basic framework of quantum mechanics and its application to the most important quantum systems: the harmonic oscillator and the hydrogen atom. When solving the problem sheets and during the problem classes, you will practice using the mathematical framework and will widen your knowledge of relevant quantum systems. This is assessed in a final exam.
GA2. Research inquiry and critical thinking
The problem sheets and the discussions during the problem classes will equip you with the ability to contribute as members of a group of researchers in a quantum-related field. This includes the ability to approach problems in a group, to present solutions efficiently and to improve a solution during the discussion.
GA5. Communication
Communication skills will be developed via two tasks: Firstly during the problems classes, you will work in groups, to learn to communicate using the appropriate mathematical terms, present the solution to a given problem and answer related questions without further preparation. Secondly, you will solve a significant problem as a group, which you will then present to the class.
Teaching and learning strategies
This subject is organised into a weekly 2-hour lecture and a 2-hour weekly class led by a tutor.
Pre-learning: Prior to the lectures you will be given pre-work in the form of additional reading, problems questions and research tasks (some content will be obtained via UTSOnline). Some of the pre-work will also be crucial to complete prior to entering the subsequent classes. At the start of the lectures you will be assessed on your comprehension of the pre-learning through Q+A, quizzes and discussion. To give an example: the last century has provided diverse developments in the field of quantum mechanics. As part of the pre-learning in the physics section you will be asked to research historical developments in quantum mechanics and present the findings to the class verbally.
Formative feedback and group work: At the end of each lecture, a set of problems is issued for you to solve outside of classes. These problem sheets are intended as practice to gain formative feedback on your understanding and progress in the subject. You are strongly encouraged to solve the problem sheets in groups provided that every group member contributes and fully understands the group's solution. This task also aims to develop team work skills within an academic environment. You will solve three graded problem sheets throughout the semester and you will verbally present the solutions to one of the problem sheets back to the class (which will be graded). This is to promote communication skills between team members but also to practice presentation skills in front of a class.
Written Essay: You will submit a written piece of work on a topic in Quantum Physics. This will be developed with assistance from tutors during the second half of the subject. The aim is to help you develop academic and professional language skills required to succeed at University and in the workplace. An emphasis in this assessment item is placed on articulating difficult quantum concepts through writing, as opposed to purely appreciating the mathematics. This is a milestone task that will assess your English language proficiency.
Content (topics)
This subject will cover the following content:
1. basic mathematical formalism of quantum mechanics
2. the Schroedinger equation both in operator notation and as a partial differential equation in the wave-function representation
3. solutions to one-dimensional problem (quantum well, scattering problems, harmonic oscillator) and examples where these problem appear in science and technology
4. the stationary states and the energy levels of the hydrogen atom, atomic transitions
Assessment
Assessment task 1: Problem solving assignments
| Intent: | This assessment task address graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1 and 2 This assessment task contributes to the development of course intended learning outcome(s): 2.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Group, individually assessed |
| Weight: | 25% |
| Criteria: | accuracy of calculations, clarity of report, clarity of presentation. |
Assessment task 2: Exam
| Intent: | This assessment task addresses graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1 and 2.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 50% |
| Criteria: | Correctness of solution, description (in words) of the physical intepretation of the quantum system. |
Assessment task 3: Written assignment
| Intent: | This assessment task addresses graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1 and 2.1 |
| Type: | Essay |
| Groupwork: | Individual |
| Weight: | 25% |
| Criteria: | Grade will be asertained with regards to a marking rubric available to the students prior to starting the assignment |
Minimum requirements
In order to pass this subject, students must receive at least 40% in the final exam and receive at least 50% overall, otherwise an "X" grade will be given.
Required texts
Mcintyre, D., Manogue, C.A., Tate, J., 2014, Quantum Mechanics: Pearson New International Edition, 1st edition, Pearson (Intl)
OR
Mcintyre, D., Manogue, C.A., Tate, J., 2012, Quantum Mechanics: A Paradigms Approach, 1st editions, Pearson
Recommended texts
-
A. Messiah, Quantum Mechanics, Dover Publications 2014
- A.C. Phillips, Introduction to Quantum Mechanics, Wiley 2003
- S. Gasiorowicz, Quantum Physics, Wiley 2003
- John S Townsend, A Modern Approach to Quantum Mechanics, University Science Books 2000
- David J. Griffiths, Introduction to Quantum Mechanics, Prentice Hall 1995
- J.J. Sakurai, Modern Quantum Mechanics, Prentice Hall 1993
-
C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics, Wiley 1977