Klein-Gordon and Dirac Bound States with Vector and Scalar Type-III Exponential Potentials

论文发布时间：[2009-11-13] 范文大全编辑：Voive.net

所有作者：田文杰

作者单位：陕西师范大学物理学与信息技术学院

论文摘要：This paper analyzes the relativistic bound states with the direct coupling of a vector and a scalar type-III exponential potentials， viz $(potential-III)$， for particular under the coupling of $V(r)=S(r)$ for $s$-wave states with vanishing centrifugal effect。 To solve the Klein-Gordon equation(KGE) under such circumstances is the crucial work， and manifold variable-transformations (independent and dependent) lead to an object equation which has the familiar structure of confluent hypergeometric equation。 Among the transformations， the technique of flexible parameters is employed as a key step of simplification。 Also， $V_１$ is restricted to the semi-field $mathbb{R}+$ to obtain an effective ansatz of the solution。 The normalization requirement excludes Kummer\\\\\\\'s function of the second type as a component of the eigenfunction， and breaks off Kummer\\\\\\\'s function of the first kind to a polynomial， as a consequence of which it also gives rise to the energy spectrum。 Yet， considering that it\\\\\\\'s the solution of a quartic algebraic equation， an implicit formalism is used for compactness and brevity。 Subsequently， bound states of Dirac equation(DE) based on the complete set $[hat{H}，hat{kappa}，hat{mathbf{J}}２，hat{mathbf{J}}_z]$ are calculated。 The specific coupling manner and $s$-wave condition lead to the identical radial DE with that of KGE， which yields the solution for the up component straightforwardly， and whereafter induces the down component。

关键词： Relativistic Wave Equations Type-III Exponential Potentials Bound States Confluent Hypergeometric Eq

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