# PHYSICS 335 : Quantum Mechanics

## Science

##### 2020 Semester Two (1205) (15 POINTS)

### Course Prescription

### Course Overview

This course provides a comprehensive development of nonrelativistic quantum mechanics at the level of wavefunctions and the Schrödinger equation, with an elementary introduction to Dirac notation; it covers the mathematical formalism, its physical interpretation, and applications to simple examples such as 1-D square-well potentials, the 1-D harmonic oscillator, and the central potential. The full mathematical framework is set out, including eigenvalue problems, compatible and incompatible observables, measurement and Heisenberg uncertainty, and the related Bell inequalities. The course aims to provide a thorough understanding of how the abstract formalism connects to the results of laboratory experiments, and a firm grounding in general principles for advancing students to build upon, in particular, students who plan postgraduate study in advanced quantum mechanics, quantum field theory, or the more applied fields of condensed matter physics and quantum optics/information.

### Course Requirements

### Capabilities Developed in this Course

Capability 1: | Disciplinary Knowledge and Practice |

Capability 2: | Critical Thinking |

Capability 3: | Solution Seeking |

Capability 4: | Communication and Engagement |

Capability 5: | Independence and Integrity |

### Learning Outcomes

- Explain how particles are represented in quantum mechanics by waves; describe the relationship between the energy and momentum of a particle and the properties of the wave representing it. (Capability 1)
- Discuss the physical meaning of the Schrödinger wavefunction and how it relates to the statistical interpretation of quantum mechanics and the fundamental difference between it and classical mechanics. (Capability 1 and 2)
- Write down the Schrödinger wave equation in its time-dependent and time-independent forms; explain how the energy representation is used to solve the time-dependent equation; apply the method to elementary examples. (Capability 1 and 3)
- Illustrate with examples how physical observables are represented by operators acting on wavefunctions; explain how the operator eigenvalues and eigenfunctions connect the mathematical formalism of quantum mechanics to measurements in the lab. (Capability 1)
- Derive the eigenvalue spectra of physical observables for exactly solvable examples like the square well potential, the harmonic oscillator, and a general angular momentum. (Capability 1 and 3)
- Outline the quantum theory of angular momentum (orbital and spin) and apply it to fundamental examples like the Stern-Gerlach effect, the central potential, and Bell inequalities. (Capability 1 and 3)
- Use Dirac notation. (Capability 1)
- Apply approximate methods, in particular time-independent and -dependent perturbation theory, to the solution of practical problems, e.g., in atomic physics, the interaction of atoms with light, and scattering from a potential. (Capability 1 and 3)
- Devise an appropriate mathematical strategy to solve a problem set out in physical terms, possibly consulting online resources and/or fellow students. (Capability 3 and 5)
- Present written solutions to assigned problems in a thoroughly argued manner, setting out the method used and all essential steps taken in a logical sequence. (Capability 4 and 5)

### Assessments

Assessment Type | Percentage | Classification |
---|---|---|

Coursework | 50% | Individual Coursework |

Final Exam | 50% | Individual Examination |

2 types | 100% |

Assessment Type | Learning Outcome Addressed | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

Coursework | ||||||||||

Final Exam |

### Learning Resources

*Quantum Mechanics*, F. Mandl (Wiley, New York, 1992)

*Introduction to Quantum Mechanics*, 2nd edition, D. J. Griffiths (Prentice Hall, New Jersey,2004)

*Introduction to Quantum Mechanics*, 3rd edition, D. J. Griffiths and D. F. Schroeter (Cambridge University Press, Cambridge, 2018)

### Workload Expectations

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For this course, you can expect 3 hours of lectures per week, where every 6th lecture takes the form of a tutorial/problem solving session. Each week you can expect to spend 3 hours on reading and thinking about the content and 4 hours of work on assignments and/or exam preparation.

### Digital Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

### Copyright

The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

### Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.

### Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website at http://disability.auckland.ac.nz

### Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page: https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.

This should be done as soon as possible and no later than seven days after the affected test or exam date.

### Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

### Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter (https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html).

### Disclaimer

Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.