Quantum equivalent of the Bertrand's theorem

Citation
N. Gurappa et al., Quantum equivalent of the Bertrand's theorem, MOD PHY L A, 15(30), 2000, pp. 1851-1857
Citations number
15
Categorie Soggetti
Physics
Journal title
MODERN PHYSICS LETTERS A
ISSN journal
02177323 → ACNP
Volume
15
Issue
30
Year of publication
2000
Pages
1851 - 1857
Database
ISI
SICI code
0217-7323(20000928)15:30<1851:QEOTBT>2.0.ZU;2-2
Abstract
A procedure for constructing general bound state potentials is given. Analo gous to the Bertrand's theorem in classical mechanics, we then identify rad ial eigenvalue problems possessing exact solvability and infinite number of eigenstates. Akin to the classical result, the only special cases of the g eneral central potential, satisfying the above two conditions, are the Coul omb and harmonic oscillator potentials.