2020/04/18 by Slimane Zaim, Zaim, S., H. Rezki +1
Physics and Astronomy · #FOS: Physical sciences #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2004.08687
openalex publication_date 2020/04/18 · openalex created_date 2020/04/24 · openalex updated_date 2026/07/28
In this work we obtain the exact solution for relativistic Landau problem plus oscillator potential in a complex symmetric gauge field in a non-commutative complex space, using the algebraic techniques of creation and annihilation operators. It is shown that the relativistic Landau problem in a complex symmetric gauge field in a non-commutative complex space is similar behavior to the Pauli equation in the presence of a symmetric gauge field in a commutative ordinary space. We derive the exact non-commutative Landau and oscillator energy levels, while the non-relativistic limit of the energy spectrum is obtained. We show that the energy is not degenerate and is splitted into two levels, as in the Zeeman effect.