Exploring the quantum realm: How does noncommutativity alter the behavior of a two-dimensional central field? This theoretical study delves into quantum mechanics within a noncommutative plane, offering new insights into the behavior of particles under a central force. It starts with an investigation of a general two-dimensional central field. For large values of the noncommutative parameter (θ), the theory can be solved perturbatively. Explicit expressions for the eigenstates and eigenvalues are derived, providing a detailed understanding of the system’s quantum states. An explicit Green function was obtained and shown that it can be expressed as an infinite series. Ultimately, the research explores the limit cases and implications of these findings. For polynomial-type potentials, a smooth limit is found for small values of θ, while nonpolynomial potentials exhibit an abrupt transition. The Landau problem is also considered as a limit case of a noncommutative system, furthering the study into these applications.
Published in the International Journal of Modern Physics A, this research aligns seamlessly with the journal’s focus on cutting-edge theoretical physics. By exploring noncommutative quantum mechanics and providing explicit solutions for a two-dimensional central field, this paper significantly contributes to the advancement of theoretical knowledge in particle physics, a key area covered by the journal.