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Unit information: Quantum Mechanics in 2024/25

Please note: Programme and unit information may change as the relevant academic field develops. We may also make changes to the structure of programmes and assessments to improve the student experience.

Unit name Quantum Mechanics
Unit code MATH35500
Credit points 20
Level of study H/6
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Schubert
Open unit status Not open
Units you must take before you take this one (pre-requisite units)

Either MATH20101 Ordinary Differential Equations 2 or MATH20402 Applied Partial Differential Equations 2

Units you must take alongside this one (co-requisite units)

None

Units you may not take alongside this one

None

School/department School of Mathematics
Faculty Faculty of Science

Unit Information

Why is this unit important?

Quantum mechanics forms the foundation of 20th century and present-day physics, and most contemporary disciplines, including atomic and molecular physics, condensed matter physics, high-energy physics, quantum optics and quantum information theory, depend essentially upon it. Quantum mechanics is also the source and inspiration for various fields in mathematical physics and pure mathematics.

The aim of the unit is to provide mathematics students with a thorough introduction to nonrelativistic quantum mechanics, with emphasis on the mathematical structure of the theory. Additionally, in conjunction with other units, it should provide suitably able and inclined students with the necessary background for further study and research at the postgraduate level. Two relevant research fields, namely quantum chaos and quantum information theory are at present strongly represented in the Mathematics Department and in the Science Faculty as a whole.

How does this unit fit into your programme of study?

This unit cannot be taken by students who have taken or are taking relevant physics units at either Level 5 or Level 6. For mathematics students, it is a prerequisite for the Level M unit Advanced Quantum Theory and a useful preparation for the Level H/6 unit Quantum Information Theory.

Your learning on this unit

An overview of content

The unit will cover:

  • the time-independent and time-dependent Schroedinger equations, and their interpretations,
  • the mathematical framework for quantum mechanics: Hilbert space, self-adjoint operators, unitary operators, commutation relations and Dirac notation,
  • the probabilistic interpretation of quantum states and the measurement process,
  • the relation between quantum and classical mechanics
  • fundamental examples of quantum systems: the free particle, tunnelling, the harmonic oscillator, central potentials and angular momentum, spin.


How will students, personally, be different as a result of the unit.

At the end of the unit the students will have improved their logical thinking, learnt to synthesize ideas from different disciplines, and have increased the range and scope of their problem-solving techniques.

Learning Outcomes

At the end of the unit the student should be able to:

  • express the physical axioms of quantum mechanics mathematically and analyse their consequences.
  • solve the Schroedinger equation for a range of problems and be able to interpret the results in physical terms.
  • explain the probabilistic interpretation of quantum states and basic aspects of the relation between classical and quantum mechanics

How you will learn

The unit will be taught through a selection of lectures, flipped-classroom, online materials, independent activities such as problem sheets and other exercises, problem classes, support sessions and office hours.

How you will be assessed

Tasks which help you learn and prepare you for summative tasks (formative):

Weekly problem sheets

Tasks which count towards your unit mark (summative):

90% Timed examination, 10% Coursework

When assessment does not go to plan

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).

The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH35500).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the University Workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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