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Upper limit on the number of bound states of the spinless Salpeter equation

Fabian Brau
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Abstract

We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the ultrarelativistic case ($m=0$), for the existence of at least one $\ell$-wave bound states: $C(\ell,p/(p-1))$ $\int_0^{\infty}dr r^{p-1} |V^-(r)|^p\ge 1$, where $C(\ell,p/(p-1))$ is a known function of $\ell$ and $p>1$.

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Fabian Brau. 2004-01-12. Upper limit on the number of bound states of the spinless Salpeter equation. https://doi.org/10.1016/s0375-9601(03)00809-0

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