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PH4038   Lagrangian and Hamiltonian Dynamics

Academic year(s): 2025-2026

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 10

Semester: 2

Availability restrictions: Not automatically available to General Degree students

The module covers the foundations of classical mechanics as well as a number of applications in various areas. Starting from the principle of least action, the Lagrangian and Hamiltonian formulations of mechanics are introduced. The module explains the connection between symmetries and conservation laws and shows bridges between classical and quantum mechanics. Applications include the central force problem (orbits and scattering) and coupled oscillators.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass PH3081 or pass PH3082 or ( pass MT2506 and pass MT2507 )

Anti-requisite(s): You cannot take this module if you take MT4507

Learning and teaching methods and delivery

Weekly contact: 3 lectures or tutorials

Scheduled learning hours: 32

Guided independent study hours: 118

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 75%, Coursework = 25%


Re-assessment: Oral Re-assessment, capped at grade 7

Intended learning outcomes

  • Formulate and apply the Lagrangianto solve the equations of motions for many systems subject to the Principle of Least Action
  • Calculate conserved quantities from symmetries
  • Calculate the Hamiltonian and establish Hamilton’s equations
  • Become familiar with canonical transformations and Hamilton-Jacobi theory
  • Understand the concept of phase space and the conservation of phase-space density (Liouville's theorem)
  • Acquire a deep knowledge of the Hamiltonian formalism that is crucial for the formulation and understanding of quantum mechanics

Additional information from school

For guidance on AS and PH modules please consult the School Handbook, at https://www.st-andrews.ac.uk/physics-astronomy/students/ug/timetables-handbooks/