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The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra
The family F L κ of all potentials V(x) for which the Hamiltonian H=−d 2 /dx 2 +V(x) in one space dimension possesses a high-order Lie symmetry is determined. A subfamily F SGA (2) of F L κ , which contains a class of potentials allowing a realization of so(2,1) as spectrum generating algebra of H t...
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| Published in: | Journal of mathematical physics 1999-10, Vol.40 (10), p.4995-5003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | The family
F
L
κ
of all potentials
V(x)
for which the Hamiltonian
H=−d
2
/dx
2
+V(x)
in one space dimension possesses a high-order Lie symmetry is determined. A subfamily
F
SGA
(2)
of
F
L
κ
,
which contains a class of potentials allowing a realization of
so(2,1)
as spectrum generating algebra of H through differential operators of finite order, is identified. Furthermore and surprisingly, the families
F
SGA
(2)
and
F
L
κ
are shown to be related to the stationary KdV hierarchy. Hence, the “harmless” Hamiltonian H connects different mathematical objects: high-order Lie symmetry, the realization of
so(2,1)
-spectrum generating algebra and families of nonlinear differential equations. We describe in a physical context the interplay between these objects. |
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| ISSN: | 0022-2488 1089-7658 |
| DOI: | 10.1063/1.533011 |