Integrable and superintegrable systems of cylindrical type in magnetic fields

Kubů, Ondřej

Integrable and superintegrable systems of cylindrical type in magnetic fields

Ondřej Kubů
(
- CTU, Prague
)

2020

103 pages

Thesis: Master

CTU, Prague

(2020)

e-Print:

2210.02393 [nlin.SI]

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Abstract: (arXiv)

The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find all quadratically integrable systems of the cylindrical type. Among them we search for systems admitting additional integrals of motion. We find all systems with an additional first order integral both in classical and quantum mechanics. It turns out that all these systems have already been known and no other exist. We also find all systems with an additional integral of type

L^2+\ldots

, respectively

L_y p_y-L_x p_y+\ldots

, of which the majority is new to the literature. All found superintegrable systems admit the first order integral

L_z

and we solve their Hamilton-Jacobi and Schrödinger equations by separation of variables in the cylindrical coordinates, for the first order systems in the Cartesian coordinates as well.

Note:

Master's thesis, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, September 2020. 103 pages, 4 figures

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