相对论自旋为0的多项式势Feshbach-Villars方程
Relativistic Spin-0 Feshbach-Villars Equations for Polynomial Potentials
摘要：
提出了一种研究相对论自旋$0$粒子的求解方法。我们采用Klein-Gordon方程的Feshbach-Villars形式，并以积分方程的形式表示。积分方程用库仑-斯特米安基表示。相应的具有库仑势和线性禁闭势的格林算符可以计算为矩阵连分式。我们考虑库仑加短程矢量势的束缚态和共振态和线性约束标量势的束缚态。该连分数在共振态能量处自然发散，但我们通过适当的解析延拓使其收敛。
英文摘要：
We propose a solution method for studying relativistic spin-$0$ particles. We adopt the Feshbach-Villars formalism of the Klein-Gordon equation and express the formalism in an integral equation form. The integral equation is represented in the Coulomb-Sturmian basis. The corresponding Green's operator with Coulomb and linear confinement potential can be calculated as a matrix continued fraction. We consider Coulomb plus short range vector potential for bound and resonant states and linear confining scalar potentials for bound states. The continued fraction is naturally divergent at resonant state energies, but we made it convergent by an appropriate analytic continuation.
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