Superintegrability in classical and quantum mechanics

About this position

Pictus PhD Fellowship Programme

Czech Technical University in Prague – International PhD Programme (PICTUS) will recruit 8 students (see Eligibility criteria below) for a full 48-month employment contract and enroll them in a specific PhD course. Candidates should prepare their own research proposal from the List of topics for the 2nd Call .

Application form should be filled and all required documents uploaded using the dedicated electronic form.

helpdesk: pictus@cvut.cz

Guide for Applicants

Superintegrability in classical and quantum mechanics

Description:

Analytical investigation of dynamical systems both in classical and quantum mechanics often employs their integrals of motion. While the notion of an integrable system can be traced back to 19th century with original applications to celestial mechanics and played an indispensable role in the formulation of quantum mechanics in early 20th century, in the last few decades there has been a growing interest in systems with more integrals of motion than needed for integrability, the so-called superintegrable systems. Their structure often implies important properties like their exact solvability without the need to solve any differential equation or separability in several coordinate systems.

The applicant can opt for one (or several) of the following topics of current interest:

• Superintegrability with higher order integrals of motion, e.g. construction and classification of such systems, their simplification by means of canonical transformations.

• Integrable and superintegrable systems in curved backgrounds, in particular with magnetic fields.

• Polynomial algebras of integrals of motion and their applications to the investigation of quantum superintegrable systems, e.g. determination of energy spectra.

Secondment:

La Trobe University, Melbourne, Victoria, Australia

Topic: polynomial algebras in the study of superintegrable systems

Co-supervisor: Dr. Ian Marquette, Senior Lecturer, Department of Mathematics and Physical Sciences