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Journal of Physics A Mathematical and General

A generalized Duffin-Kemmer-Petiau oscillator

Youcef Nedjadi, Roger C. Barrett

Published Aug 7, 1998• 42 citations
Publisher

Abstract

We propose a generic S = 1 relativisitic oscillator model which extends the class of relativistic bosonic oscillators. The Duffin-Kemmer-Petiau (DKP) oscillator we introduced in an earlier work can be recovered as an element of a family of DKP oscillators that can be realized within this generic model. We present the formalism for the exact quantum mechanical treatment of this generic model and, for illustration, compute the eigenvalues of a particular family of relativistic oscillators.

DOI
10.1088/0305-4470/31/31/016

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We propose a generic S = 1 relativisitic oscillator model which extends the class of relativistic bosonic oscillators. The Duffin-Kemmer-Petiau (DKP) oscillator we introduced in an earlier work can be recovered as an element of a family of DKP oscillators that can be realized within this generic model. We present the formalism for the exact quantum mechanical treatment of this generic model and, for illustration, compute the eigenvalues of a particular family of relativistic oscillators.
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Spin-0 and Spin-1 Bosonic Particles Dynamics in (1+3)(1+3)(1+3) Dimensions via the Relativistic DKP Equation with a Spatially-Dependent Exponential Mass Term
Abstract The Duffin-Kemmer-Petiau (DKP) equation is a relativistic wave equation governing the dynamics of spin-0 and spin-1 bosonic particles. In this work, we study the (1+3)(1+3)(1+3) ( 1 + 3 ) -dimensional DKP equation with a spatially dependent mass under a modified deformed exponential type potential. Using the framework of supersymmetric quantum mechanics, we derive approximate analytical solutions. A novel extension of the Pekeris approximation is introduced to treat the centrifugal barrier, enabling the complete determination of the energy spectrum. The non-relativistic limit of the DKP equation is obtained via an established transformation technique. The model is applied to diatomic molecules including lithium hydride (LiH), hydrogen chloride (HCl), 7Li2^{7}\textrm{Li}_{2}7Li2​ 7 Li 2 , Na2\textrm{Na}_{2}Na2​ Na 2 , and ScI. The energy spectra are computed for various quantum states ∣n,l,j⟩\left| n,l,j\right\rangle ∣n,l,j⟩ n , l , j using both relativistic and non-relativistic expressions. For LiH and HCl, where experimental data are scarce, our results show strong agreement with earlier theoretical predictions. For 7Li2^{7}\textrm{Li}_{2}7Li2​ 7 Li 2 , Na2\textrm{Na}_{2}Na2​ Na 2 , and ScI, the calculated energies align excellently with available experimental data. The proposed framework provides a reliable and analytically tractable tool for studying bosonic systems with position-dependent effective masses.