Available student project - New trends in separation of variables

Research fields

  • Theoretical Physics

Project details

It is well known that certain systems in classical mechanics are completely integrable in a sense that they possess a sufficient number of integrals of motion which allow us to integrate  equations of motion explicitly. In Hamiltonian formulation the number of integrals of motion should be no less than the number of canonical coordinates (or canonical momenta). Then there exist special canonical variables called action-angle variables such that the dynamics of the system in these coordinates reduces to a set of one-dimensional problems.

These ideas can be extended to  quantum integrable systems. In quantum case we are looking for a complete set of  eigenfunctions which simultaneously diagonalize ``quantum integrals of motion''. Quantum separation of variables allows us to express these multi-variable eigenfunctions in terms of functions of one variable only. In principle this helps to solve the equations of motions for the original system. Surprisingly such (integral) transformations are linked to some well known (or sometimes new) formulas in the theory of classical special functions.

Required background

PHYS3001, MATH2406, MATH3351

Project suitability

This research project can be tailored to suit students of the following type(s)
  • 3rd year special project
  • PhB (2nd or 3rd year)
  • Honours project
  • Vacation scholar

Contact supervisor

Mangazeev, Vladimir profile
Fellow
59475

Updated:  17 August 2017/ Responsible Officer:  Head of Department/ Page Contact:  Physics Webmaster