PH4038 Lagrangian and Hamiltonian Dynamics

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Module description

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-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS PH3081 OR PASS PH3082 OR ( PASS MT2506 AND PASS MT2507 )

Anti-requisites

YOU CANNOT TAKE THIS MODULE IF YOU TAKE MT4507

Assessment pattern

2-hour Written Examination = 75%, Coursework = 25%

Re-assessment

Oral Re-assessment, capped at grade 7

Learning and teaching methods and delivery

Weekly contact

3 lectures or tutorials

Scheduled learning hours

32

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

118

The number of hours that students are expected to invest in independent study over the period of the module.

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/