超球${δ\text{-}δ^\prime}$势
Hyperspherical ${δ\text{-}δ^\prime}$ potentials
摘要：
球对称的潜在$a \,δ(r-r_0)+b\,δ' (r-r_0)$推广的$d$维空间作为一个独特的自伴扩展的自由哈密顿的表征。对于这种扩展的狄拉克三角洲，负，零和正能量状态的频谱进行了研究，在$d\geq 2$，提供数值结果的期望值的半径作为一个功能的自由参数的潜力。值得注意的是，只有当$d=2$，对任意$a>0$的$δ'$势允许一个角动量为零的束缚态.
英文摘要：
The spherically symmetric potential $a \,δ(r-r_0)+b\,δ' (r-r_0)$ is generalised for the $d$-dimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac delta, the spectrum of negative, zero and positive energy states is studied in $d\geq 2$, providing numerical results for the expectation value of the radius as a function of the free parameters of the potential. Remarkably, only if $d=2$ the $δ$-$δ'$ potential for arbitrary $a>0$ admits a bound state with zero angular momentum.
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