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arXiv · 1806.02150

Hyperspherical ${δ\text{-}δ^\prime}$ potentials

J. M. Munoz-Castaneda·L. M. Nieto·C. Romaniega
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Abstract

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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J. M. Munoz-Castaneda, L. M. Nieto, C. Romaniega. 2018-06-07. Hyperspherical ${δ\text{-}δ^\prime}$ potentials. https://doi.org/10.1016/j.aop.2018.11.017

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