Algebraic treatments of the problems of the spin-1/2 particles in the one and two-dimensional geometry: a systematic study

Abstract

We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can be treated in a unified framework of the algebra. The systematic study presented here reproduces a number of earlier results in a natural way as well as leads to a novel findings. Possible generalizations of the method are also suggested.

arXiv commentAnnals of Physics (2005) to be published

References in corpus (10)

• Quasi-Exactly Solvable Systems and Orthogonal Polynomials
• Two electrons in an external oscillator potential: hidden algebraic structure
• An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models
• Quasi Exactly Solvable 2$\times$2 Matrix Equations
• Solution of a Hamiltonian of quantum dots with Rashba spin-orbit coupling: quasi-exact solution
• Three dimensional quadratic algebras: Some realizations and representations
• Quasi-exactly solvable models in nonlinear optics
• Quasi-exact-solution of the Generalized Exe Jahn-Teller Hamiltonian
• On algebraic classification of quasi-exactly solvable matrix models
• Differential Realizations of the Two-Mode Bosonic and Fermionic Hamiltonians: A unified Approach

Cited by in corpus (4)

• Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model
• $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry
• Solution of the Bosonic and Algebraic Hamiltonians by using AIM
• Berry phase of the Tavis-Cummings model with three modes of oscillation