Study about Matrix Quasi-Exactly Solvable Jacobi Elliptic Hamiltonian | Chapter 4 | Current Research Progress in Physical Science Vol. 5

In the last few years, a new class of operators which is intermediate to exactly solvable and non-solvable operators has been discovered: the quasi-exactly solvable (QES) operators, for which a finite part of the spectrum can computed algebraically. A new example of a 2 × 2 -matrix quasi-exactly solvable (QES) Hamiltonian was constructed which is associated with a potential depending on the Jacobi elliptic functions. The QES analytic method was applied in order to establish three necessary and sufficient algebraic conditions for the 2 × 2 -matrix Hamiltonian to have an invariant vector space whose generic elements are polynomials. This Hamiltonian is called quasi-exactly solvable.

 

Author (s) Details

Ancilla NININAHAZWE
Université du Burundi, Institut de Pédagogie Appliquée, B.P. 5223 Bujumbura, Burundi.

 

Please see the book here:- https://doi.org/10.9734/bpi/crpps/v5/2760

Quasi-exactly Solvable Extended Calogero Model | Chapter 13 | New Insights into Physical Science Vol. 2

We study a multispecies Calogero model on the line for 2 N  and 3 N . Here, we perform a gauge transformation on the Calogero Hamiltonian Hwhich leads to the new operator H ~ called the gauge one. We establish the some vector spaces of polynomials preserved by the gauge Hamiltonian in the cases of equal and different masses. The eigen values of these both cases are computed algebraically. The operator H ~ (thereforeH) is called quasi-exactly solvable.    

Author(s) Details

Ancilla Nininahazwe
Université du Burundi, Institut de Pédagogie Appliquée, B.P. 5223 Bujumbura, Burundi.

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