two-body Calogero-Moser and Calogero models
The Calogero-Moser model, the Calogero model and analytic extension.
The paper is devoted to a derivation of exact solutions to the Cauchy problem in the two-body Calogero-Moser and Calogero models. Both models are known to be the (one-dimensional) quantum integrable systems describing long-interaction of particles in physics. From the mathematical viewpoint, the solutions found are analytic in time. The author also discusses briefly Wigner's commutation relations in quantum mechanics, as well as the eigenvalue problem of the corresponding Schrödinger equation.NEWLINENEWLINE The generalized Fourier (both cosine and sine) transforms are found explicitly for the exact solutions. The author also discusses at length an embedding theorem of Sobolev type, which appears to be the natural application of the Fourier transform he derived.NEWLINENEWLINE It should be mentioned that similar solutions were derived earlier by \textit{M. Rösler} [ Commun. Math. Phys. 192, 519--542 (1998; Zbl 0908.33005)].NEWLINENEWLINEFor the entire collection see [Zbl 0963.00016].
scientific article; zbMATH DE number 1664294
scientific article