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math-ph2013★ 6 cited
A product formula for the eigenfunctions of a quartic oscillator
Martin Hallnäs, Edwin Langmann
We consider the Schrödinger operator on the real line with an even quartic potential. Our main result is a product formula of the type $ψ_k(x)ψ_k(y) = \int_{\mathbb{R}} ψ_k(z)\math…
math-ph2013★ 8 cited
Source identities and kernel functions for deformed (quantum) Ruijsenaars models
F. Atai, M. Hallnäs, E. Langmann
We consider the relativistic generalization of the quantum Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic…
nlin.SI2013
A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians
Martin Hallnäs, Simon Ruijsenaars
We obtain symmetric joint eigenfunctions for the commuting PDOs associated to the hyperbolic Calogero-Moser N-particle system. The eigenfunctions are constructed via a recursion sc…