Bosonic quasideterminants and eigenvalue problems of generalized spin-orbit operators

Abstract

This paper deals with an extension of the applications of the paper by Gelfand and Retakh [Funct. Anal. Appl. 25, 91 (1991)] on quasideterminant (QsD) algebraic method to eigenvalue problems in quantum mechanics. Using relevant identities on the free 1-mode bosonic algebra, we build characteristic QsDs associated with generalized spin-orbit Hamiltonians with a well defined representation which allows us to explicitly and straightforwardly compute analytical expressions of eigenenergies. Specific instances are provided on f-deformed generalized Jaynes–Cummings models and other Hamiltonian classes widely used in condensed matter physics.