Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 48, Issue 9, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/48/9/095205
Keywords
elliptic potential; hidden algebra; polynomial eigenfunctions; particular integral
Categories
Funding
- University Program FENOMEC
- PAPIIT grant [IN109512]
- CONACyT grant (Mexico) [166189]
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The potential of the BC1 quantum elliptic model is a superposition of two Weierstrass functions with a doubling of both periods (two coupling constants). The BC1 elliptic model degenerates to an A(1) elliptic model characterized by the Lame Hamiltonian. It is shown that in the space of the BC1 elliptic invariant, the potential becomes a rational function, while the flat space metric becomes a polynomial. The model possesses the hidden sl(2) algebra for arbitrary coupling constants: it is equivalent to the sl(2) quantum top in three different magnetic fields. It is shown that three one-parametric families of coupling constants exist, for which a finite number of polynomial eigen-functions (up to a factor) occur.
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