SU(3) Brachistochrone and the Isotropic Oscillator

Peter Morrison

doi:10.20944/preprints202306.1967.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 26 June 2023 / Approved: 27 June 2023 / Online: 28 June 2023 (09:43:37 CEST)

This paper discusses two major applications of SU(3) theory, the first being the question of quantum brachistochrones and problems in time optimal control theory, the second being the use of spherical tensor decompositions of the special functions which are associated to SU(3) via the isotropic oscillator. We discuss the derivation of the quantum brachistochrone problem more generally from the perspective of von Neumann equations and matrix mechanics, arriving at an equivalent formulation to the Lagrangian method. Discussion is given to the application of such advanced methods in quantum computation, and some future directions that may be amenable to a similar sort of an

gell-mann; calculus; quantum; control; brachistochrone; optimal; time; operator; eigenstate; eigenmatrix

Physical Sciences, Mathematical Physics

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SU(3) Brachistochrone and the Isotropic Oscillator

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