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Durham University

Faculty Handbook Archive

Archive Module Description

This page is for the academic year 2021-22. The current handbook year is 2022-23

Department: Mathematical Sciences

MATH3111: QUANTUM MECHANICS III

Type Open Level 3 Credits 20 Availability Available in 2021/22 Module Cap Location Durham

Prerequisites

  • Analysis in Many Variables (MATH2031) and Mathematical Physics II (MATH2071).

Corequisites

  • None.

Excluded Combination of Modules

  • Theoretical Physics 2 (PHYS2631) or Foundations of Physics 3a (PHYS3621).

Aims

  • To give an understanding of the reasons why quantum theory is required, to explain its basic formalism and how this can be applied to simple situations, to show the power in quantum theory over a range of physical phenomena and to introduce students to some of the deep conceptual issues it raises.

Content

  • Problems with Classical Physics: Photo-electric effect, atomic spectra, wave-particle duality.
  • Waves and the Schrodinger Equation.
  • Formal Quantum Theory: Vectors, linear operators, hermitian operators, eigenvalues, complete sets, expectation values, commutation relations, Schrodinger representations.
  • Applications in one-dimension.
  • Angular Momentum: Commutation relations, eigenvalues, states, relation to spherical harmonics.
  • Hydrogen Atom.
  • Symmetry, Antisymmetry and Exclusion Principle.
  • Conceptual Issues.
  • Approximation Methods: Peturbation Theory.

Learning Outcomes

Subject-specific Knowledge:
  • By the end of the module students will: be able to solve novel and/or complex problems in Quantum Mechanics.
  • have a systematic and coherent understanding of theoretical mathematics in the fields Quantum Mechanics.
  • have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Description of physical system in terms of state vectors.
  • Description of observables using linear hermitian operators.
  • Schrodinger equation for time evolution of system.
  • Representation of states and operators as wave functions and differential operators.
  • Relating formal theory to experimental measurements.
  • Important examples including harmonic oscillator, 1D scattering and hydrogen atom.
Subject-specific Skills:
  • In addition students will have specialised mathematical skills in the following areas which can be used in minimal guidance: Modelling.
Key Skills:

    Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

    • Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
    • Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
    • Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
    • The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

    Teaching Methods and Learning Hours

    Activity Number Frequency Duration Total/Hours
    Lectures 42 2 per week for 20 weeks and 2 in term 3 1 Hour 42
    Problems Classes 8 Four in each of terms 1 and 2 1 Hour 8
    Preparation and Reading 150
    Total 200

    Summative Assessment

    Component: Examination Component Weighting: 100%
    Element Length / duration Element Weighting Resit Opportunity
    Written examination 3 Hours 100%

    Formative Assessment:

    Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.


    Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University