Speaker
Description
We provide a Jordan algebraic, non-associative formulation of the Landau problem with a non-commutative parameter coupled to a harmonic potential as an inclusive example. To achieve this, we further extend a recent work of Schupp and Szabo (2024) to infinite dimensional Jordan algebras and the Landau problem. In particular, we present an alternative formulation of the Hilbert space version of quantum mechanics in order to obtain the Hilbert space corresponding to this problem.Choosing the coordinates as the center of the cyclotron motion, one obtains a non-commutative parameter. That parameter is then described in terms of an associator in the Jordan algebraic setting by obtaining results which are potentially applicable to other non-associative formulations as well. Moreover, pure states and density matrices arising from our construction are characterized. This in turn leads us to the explicit description of split operators for the corresponding Hamiltonian and the Jordan-Schrodinger time-evolution equation for the state vectors in this specific problem.