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MATH3111: QUANTUM MECHANICS III

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 3
Credits 20
Availability Available in 2023/24
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

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

Corequisites

  • None.

Excluded Combinations of Modules

  • Theoretical Physics 2 (PHYS2631) or Foundations of Physics3a (PHYS3621).

Aims

  • To give an understanding of the reasons why quantum theory isrequired, to explain its basic formalism and how this can be applied tosimple situations, to show the power in quantum theory over a range ofphysical phenomena and to introduce students to some of the deepconceptual 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 ExclusionPrinciple.
  • Conceptual Issues.
  • Approximation Methods: Peturbation Theory.

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will: be able to solvenovel and/or complex problems in Quantum Mechanics.
  • have a systematic and coherent understanding of theoreticalmathematics in the fields Quantum Mechanics.
  • have acquired coherent body of knowledge of these subjectsdemonstrated through one or more of the following topic areas:Description of physical system in terms of state vectors.
  • Description of observables using linear hermitianoperators.
  • Schrodinger equation for time evolution of system.
  • Representation of states and operators as wave functions anddifferential operators.
  • Relating formal theory to experimentalmeasurements.
  • Important examples including harmonic oscillator, 1D scattering and hydrogen atom.

Subject-specific Skills:

  • In addition students will have specialised mathematicalskills 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 theapplication of the theory to practical examples.
  • Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge andunderstanding.
  • Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback forthe students and the lecturer on students' progress.
  • The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week for 20 weeks and 2 in term 31 Hour42 
Problems Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 Hours100 

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.

More information

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