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

@article{Koc2005AlgebraicTO, title={Algebraic treatments of the problems of the spin-1/2 particles in the one- and two-dimensional geometry: A systematic study}, author={Ramazan Koc and Hayriye Tutunculer and Mehmet Koca and Eser Olğar}, journal={Annals of Physics}, year={2005}, volume={319}, pages={333-347} }

## 7 Citations

Sp(4, R) algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry

- PhysicsThe European Physical Journal Plus
- 2019

Abstract.In this paper we study the interaction part of the most general Hamiltonian of a two-level system in two-dimensional geometry. We decouple the equations for each spinor component and…

A solution of the bosonic and algebraic Hamiltonians by using an AIM

- Physics, Mathematics
- 2010

We apply the notion of an asymptotic iteration method (AIM) to determine the eigenvalues of the bosonic Hamiltonians that include a wide class of quantum optical models. We consider the solutions of…

Berry phase of the Tavis-Cummings model with three modes of oscillation

- PhysicsJournal of Mathematical Physics
- 2019

In this paper we develop a general method to obtain the Berry phase of time-dependent Hamiltonians with a linear structure given in terms of the $SU(1,1)$ and $SU(2)$ groups. This method is based on…

Matrix diagonalization and exact solution of the k-photon Jaynes–Cummings model

- PhysicsThe European Physical Journal D
- 2018

Abstract
We study and exactly solve the two-photon and k-photon Jaynes–Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the…

Generalized Jaynes-Cummings Model and Shape Invariant Potentials: Master Function Approach

- Physics
- 2015

In this work, we use the master function formalism and solve the generalized Jaynes-Cummings Hamiltonian for some solvable potentials. By using this approach, we apply the shape invariance properties…

Two and k-Photon Jaynes–Cummings Models and Dirac Oscillator Problem in Bargmann–Segal Representation

- Physics
- 2013

In this work, we show that the Bargmann–Segal representation is a very simple approach to obtain the energy eigenvalues of some two-level quantum systems. It is shown that for 2-photon and k-photon…

Full Analytic Spectrum of Generalized Jaynes-Cummings Hamiltonians

- PhysicsTheoretical and Mathematical Physics
- 2019

We develop an analytic formalism using basic quantum mechanics techniques to successfully solve the multiphoton Jaynes–Cummings and the generalized Dicke Hamiltonians. For this, we split the…

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