Complete set of eigenfunctions of the quantum Toda chain

DOI10.1007/s11005-009-0296-5zbMath1161.81383OpenAlexW2072368770MaRDI QIDQ1013637

Daniel An

Publication date: 20 April 2009

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-009-0296-5

zbMATH Keywords

quantum integrable systemsWhittaker functionsAgmon metricBaxter equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (6)

Exact quantization conditions for the elliptic Ruijsenaars-Schneider model ⋮ Exact relativistic Toda chain eigenfunctions from separation of variables and gauge theory ⋮ Splitting of surface defect partition functions and integrable systems ⋮ Spectral theory and mirror curves of higher genus ⋮ Aspects of the inverse problem for the Toda chain ⋮ Unitarity of the SoV transform for the Toda chain

Cites Work

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• Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. V: Lower bounds and path integrals
• Integral representation for the eigenfunctions of a quantum periodic Toda chain
• Integral representations for the eigenfunctions of quantum open and periodic Toda chains from the QISM formalism
• The periodic Toda chain and a matrix generalization of the Bessel function recursion relations
• Laplace's Integral, the Gamma Function, and beyond

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