https://doi.org/10.1140/epjc/s10052-009-0886-5
Regular Article - Theoretical Physics
Quantum Hall effect in noncommutative quantum mechanics
1
School of Physics Science and Technology, Xinjiang University, Urumqi, 830046, China
2
Department of Physics, Hangzhou Normal University, Hangzhou, 310036, China
3
The Abdus Salam International Center for Theoretical Physics, Trieste, Italy
* e-mail: dulat98@yahoo.com
Received:
1
September
2008
Revised:
8
December
2008
Published online:
31
January
2009
We study the quantum Hall (QH) effect for an electron moving in a plane whose coordinates and momenta are noncommuting under the influence of uniform external magnetic and electric fields. After solving the time independent Schrödinger equation both on a noncommutative space (NCS) and a noncommutative phase space (NCPS), we obtain the energy eigenvalues and eigenfunctions of the relevant Hamiltonian. We derive the electric current whose expectation value gives the QH effect both on a NCS and a NCPS.
PACS: 02.40.Gh – / 11.10.Nx – / 03.65.-w –
© Springer-Verlag, 2009
