Exact Solution of D-Dimensional Klein-Gordon Oscillator with  Minimal Length

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Exact Solution of D-Dimensional Klein-Gordon Oscillator with Minimal Length

Y. Chargui,¹ L. Chetouani,² and A. Trabelsi^1,3

¹Unité de Recherche de Physique Nucléaire et des Hautes Energies, Faculté des Sciences de Tunis, 1080 Tunis, Tunisia

²Département de Physique Théorique, Institut de Physique, Université de Constantine, Route Ain El Bey, Constantine, Algeria

³Centre National des Sciences et Technologies Nucléaires, Technopole de Sidi-Thabet 2020, Tunisia

Received: 2009-02-16 Revised: 1900-01-01 Published: 2010-02-15

Abstract

Abstract: Specific modifications of the usual canonical commutation relations between position and momentum operators have been proposed in the literature in order to implement the idea of the existence of a minimal observable length. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentum space representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and the
corresponding momentum space wave function are obtained. Following
Chang et al. (Phys. Rev. D 65 (2002) 125027), we discuss constraint that can be placed on the minimal length by measuring the energy levels of an
electron in a penning trap.

Key words: Klein-Gordon oscillator, minimal length, energy spectrum

PACS numbers:

02.40.Gh

Y. Chargui, L. Chetouani, and A. Trabelsi,, Commun. Theor. Phys. 53 (2010) 231.

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Exact Solution of D-Dimensional Klein-Gordon Oscillator with Minimal Length

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