Abstract
A new example of PT-symmetric quasi-exactly solvable (QES) 22×-matrix Hamiltonian which is associated to a trigonometric Razhavi potential is con-sidered. Like the QES analytic method considered in the Ref. [1][2], we es-tablish three necessary and sufficient algebraic conditions for this Hamilto-nian to have a finite-dimensional invariant vector space whose generic ele-ment is polynomial. This non hermitian matrix Hamiltonian is called qua-si-exactly solvable [3].
Highlights
A new example of PT-symmetric quasi-exactly solvable (QES) 2 × 2 -matrix Hamiltonian which is associated to a trigonometric Razhavi potential is considered
Like the QES analytic method considered in the Ref. [1] [2], we establish three necessary and sufficient algebraic conditions for this Hamiltonian to have a finite-dimensional invariant vector space whose generic element is polynomial
Several problems in quantum physics lead to the main mathematical challenge of constructing the spectrum of a linear operator defined on an appropriate vector space of functions which belongs to a suitable domain of Hilbert space
Summary
Several problems in quantum physics lead to the main mathematical challenge of constructing the spectrum of a linear operator defined on an appropriate vector space of functions which belongs to a suitable domain of Hilbert space. In most cases, this type of problem cannot be analytically solved, in other words, all eigenvalues of the Hamiltonian cannot be computed algebraically. In the last few years, a new class of operators has been discovered. This class is intermediate between exactly solvable operators and non solvable operators. Its name is the quasi-exactly solvable (QES) operators [3]-[8], for which a finite part of the spectrum can be computed algebraically
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
