2014/08/31 by Alexander V. Turbiner, A V Turbiner · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Coupling (piping) #Coupling constant #Eigenfunction #Elliptic rational functions #Modular elliptic curve #Polynomial #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Superposition principle #hep-th #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/9/095205
published as Journal of Physics A 48 (2015) 192002 · 10 pages, some references added, introduction extended
arxiv created 2014/12/14 · openalex publication_date 2015/02/10 · openalex created_date 2016/06/24 · arxiv updated 2016/06/30 · openalex updated_date 2026/08/06
The potential of the BC 1 quantum elliptic model is a superposition of two Weierstrass functions with a doubling of both periods (two coupling constants). The BC 1 elliptic model degenerates to an A 1 elliptic model characterized by the Lamé Hamiltonian. It is shown that in the space of the BC 1 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 eigenfunctions (up to a factor) occur.