Undergraduate Course: Quantum Mechanics for Mathematicians (MATH10107)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 4 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  This is a basic course on quantum mechanics for mathematics students, departing from the basic postulates and discussing a number of examples which illustrate the key role played by linearity. 
Course description 
The discovery of the quantum theory of nature is arguably the most farreaching scientific revolution of the twentieth century. In the first quarter of that century it became apparent that everyday assumptions about the nature of the world begin to break down when objects the size of atoms are involved.
It is the mathematics of the quantum world which is the main subject of this course. The basic ideas are now readily accessible at the undergraduate level and provide a marvellous illustration of the importance of linear spaces, linear operators, eigenvalues and differential equations in a central context in modern mathematics. (It is not intended to go into technical detail about infinitedimensional spaces etc). This course does, however, motivate the need for a precise theory of selfadjoint operators in infinitedimensional spaces.
Apart from its intrinsic interest, a further justification for this course is that quantum ideas are now becoming important in many areas of pure mathematics: quantum groups (algebra), quantum cohomology (topology/geometry), quantum cryptography, quantum information.
The course will include (some of) the following topics:
 Basic postulates of quantum theory, wave function, probabilistic interpretation, Dirac notation
 Schrödinger equation and examples: potentials, bound states, tunnelling.
 Operators, Heisenberg uncertainty principle, correspondence principle. Harmonic oscillator, wave packets, dispersion.
 Symmetries in quantum theory: hydrogenic atoms and their spectrum
 Scattering, WKB approximation

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 18,
Supervised Practical/Workshop/Studio Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
73 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
No Exam Information 
Learning Outcomes
On completion of this course, the student will be able to:
 Be fully conversant in the basic concepts of quantum theory: wave function, probabilistic interpretation
 Solve the Schrödinger equation in some simple potentials and interpret the states
 Solve harmonic oscillatorlike systems using operators and verify the uncertainty and correspondence principles in simple cases
 Apply symmetry considerations to solve for the spectrum of simple systems
 Solve simple scattering problems

Reading List
Recommended in addition to materials provided:
 (*)Brian Hall, Quantum Theory for Mathematicians, Springer 2013 (Selected chapters)
 Keith Hannabuss, An introduction to Quantum Theory, OUP 1997
(*) available to download from the University Library 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  QMM,Quantum mechanics,Schrödinger equation,Heisenberg uncertainty principle 
Contacts
Course organiser  Dr Joan Simon Soler
Tel: (0131 6)50 8571
Email: J.Simon@ed.ac.uk 
Course secretary  

