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

Jacobi Elliptic Potential and Quasi-Exact Solvability| Chapter 3 | New Frontiers in Physical Science Research Vol. 3

 A new illustration of a Jacobi elliptic potential-connected quasi-exactly explainable 2 × 2 matrix Hamiltonian is grown. In order for the Jacobi Hamiltonian to have a finite dimensional even vector space, we must placate three necessary and sufficient tests, which we estimate algebraically using the QES analytic approach. It is refer to as being "quasi-exactly explainable" for the matrix Jacobi Hamiltonian.

Author(s) Details:

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

Please see the link here: https://stm.bookpi.org/NFPSR-V3/article/view/8588