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

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

2004-02-10

arxiv.org/abs/math-ph/0402023v1

Phys. Lett. A322, 67 (2004)

Physics

Mathematical Physics

Scientific paper

10.1016/j.physleta.2004.01.005

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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