MAS324 Milestones in Applied Mathematics II: Quantum Theory

Semester 2, 2017/18 10 Credits
Lecturer: Dr Eun-jin Kim Reading List
Aims Outcomes Teaching Methods Assessment

The development of quantum theory revolutionized both physics and mathematics during the 20th century. The theory has applications in many technological advances, including: lasers, super-conductors, modern medical imaging techniques, transistors and quantum computers. This course introduces the basics of the theory and brings together many aspects of mathematics: for example, probability, matrices and complex numbers. Only first year mechanics is assumed, and other mathematical concepts will be introduced as they are needed.

Prerequisites: MAS112 (Vectors and Mechanics)
Not with: PHY202 (Quantum Mechanics)
No other modules have this module as a prerequisite.


Outline syllabus

  • Historical introduction: Brief introduction to the experiments leading to the development of quantum theory and motivation of Schrodinger's equation.
  • Simple quantum systems: Particle in an infinite potential well, stationary states, expectation values, conservation of probability; simple scattering, potential step, potential barrier, finite potential well; 2-D potential well, degeneracy; finite-dimensional quantum systems.
  • Mathematical aspects of quantum theory: Position and momentum operators; commutation relations; uncertainty principle; quantum simple harmonic oscillators



Aims

  • To introduce the subject of quantum mechanics;
  • To study simple quantum systems;
  • To introduce some of the historical aspects of the subject.

Learning outcomes

    Teaching methods

    Lectures


    20 lectures, no tutorials

    Assessment

    One formal 2 hour written examination.

    Reading list

    Type Author(s) Title Library Blackwells Amazon
    B Bransden and Joachain Introduction to Quantum Mechanics 530.12 (B) Blackwells Amazon
    B Davies Quantum Mechanics 530.12 (D) Blackwells Amazon
    B Rae Quantum Mechanics 530.12 (R) Blackwells Amazon

    (A = essential, B = recommended, C = background.)

    Most books on reading lists should also be available from the Blackwells shop at Jessop West.