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On the decrease of the number of bound states with the increase of the angular momentum

Fabian Brau
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Abstract

For the class of central potentials possessing a finite number of bound states and for which the second derivative of $r V(r)$ is negative, we prove, using the supersymmetric quantum mechanics formalism, that an increase of the angular momentum $\ell$ by one unit yields a decrease of the number of bound states of at least one unit: $N_{\ell+1}\le N_{\ell}-1$. This property is used to obtain, for this class of potential, an upper limit on the total number of bound states which significantly improves previously known results.

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Fabian Brau. 2004-02-10. On the decrease of the number of bound states with the increase of the angular momentum. https://doi.org/10.1016/j.physleta.2004.01.005

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