Eur. Phys. J. C (2008) 56: 597-606
https://doi.org/10.1140/epjc/s10052-008-0681-8

Regular Article - Theoretical Physics

Landau analog levels for dipoles in non-commutative space and phase space

Landau analog levels for dipoles

¹ Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, PB, Brasil
² Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, SP, Brazil

^* e-mail: furtado@fisica.ufpb.br

Received: 4 March 2008
Revised: 11 July 2008
Published online: 31 July 2008

Abstract

We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and magnetic dipole moments, interacts with the fields via the Aharonov–Casher and He–McKellar–Wilkens effects. For this model we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the usual non-commutative space coordinates.