The accidental degeneracy problem in nonrelativistic quantum mechanics

Khare, Avinash (1983) The accidental degeneracy problem in nonrelativistic quantum mechanics Journal of Mathematical Physics, 24 (4). pp. 867-873. ISSN 0022-2488

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Official URL: http://jmp.aip.org/resource/1/jmapaq/v24/i4/p867_s...

Related URL: http://dx.doi.org/10.1063/1.525763

Abstract

I show that the class of potentials given by V(r)=Ar2d-2-Brd-2 possesses partial accidental degeneracy given by En1,l2=En2,l1 in case d=(l2-l1)/(n2-n1), B=[l+dn+(1-d)/2](2A/μ)½. It is further shown that, for a given potential, as the number of dimensions change, the accidental degeneracy pattern also changes except when d=1 and 2. Using these results, it is then shown that for the bottom quark-antiquark (bb̅) bound system, most likely E3S<E1F<E2D. Finally I also make some conjectures about the ordering of levels for a wide class of potentials.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Quantum Mechanics; Degeneration; Potentials; Quarks; Bound State
ID Code:83397
Deposited On:20 Feb 2012 08:45
Last Modified:20 Feb 2012 08:45

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