Classical and quantum mechanical systems of Toda-lattice type. III: Joint eigenfunctions of the quantized systems

DOI10.1007/BF01205939zbMath0616.22010MaRDI QIDQ1821213

Nolan R. Wallach, Roe Goodman

Publication date: 1986

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

zbMATH Keywords

Weyl groupHamiltonianSchrödinger operatorDynkin diagramToda lattice typejoint eigenfunctionsfinite root system

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Simple, semisimple, reductive (super)algebras (17B20) Miscellaneous applications of functional analysis (46N99)

Related Items

Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure, Asymptotic expansions of matrix coefficients of Whittaker vectors at irregular singularities, Quantum cohomology of the infinite-dimensional generalized flag manifolds, Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit, On the complete integrability of the periodic quantum Toda lattice, Aspects of the inverse problem for the Toda chain, Unitarity of the SoV transform for the Toda chain, Integrable boundary interactions for Ruijsenaars' difference Toda chain, On the spectral resolution of the quantum Toda lattice, Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions, On the quantum \(\mathfrak{osp}(1|2\ell)\) Toda chain, Higher-Order Sugawara Operators for Affine Lie Algebras

Cites Work

• Unnamed Item
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• Whittaker functions on semisimple Lie groups
• Classical and quantum mechanical systems of Toda-lattice type. II: Solutions of the classical flows
• Finite-zone, almost-periodic solutions in WKB approximations
• Elliptic and subelliptic estimates for operators in an enveloping algebra
• Whittaker vectors and conical vectors
• Classical and quantum-mechanical systems of Toda lattice type. I
• On Whittaker vectors and representation theory
• Representation of Elliptic Operators in an Enveloping Algebra
• Spherical Functions on a Semisimple Lie Group, I
• Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle.