Abstract
We consider the problem of a quantum mechanical particle in R 3 interacting with N point sources which move on preassigned smooth paths. We prove that this problem has a unique weak solution, and we provide for it an explicit representation. Moreover we show that the corresponding flow is unitary.
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References
Adami R., Teta A. A simple model of concentrated non linearity (preprint mp-arc 99.86)
Albeverio S, Gesztesy F., Hoegh-Krohn R, Holden H, Solvable models in Quantum Mechanics Springer Verlag New York 1988
Albeverio S, Kurasov P. Singular perturbations of differential operators, book to be published (preliminary copy, Dec 1998)
Dell’Antonio G.F., Figari S., Teta A, Hamiltonian for systems of N article interacting through point interactions, Ann. Inst. H.Poincare, 60, 253–290
[Dell’Antonio G.F., Figari S., Teta A, A limit evolution problem for time-dependent point interactions J.Funct. Analysis, 142, 249–275
Dell’Antonio G.F., Figari S., Teta A, Diffusion of a particle in presence of N moving point sources, Ann. Inst. H.Poincare 69, 413–424
Dell’Antonio G.F., Figari S., Teta A, Schroedinger equation with moving point interactions in three dimensions, preprint Sissa
[Merle K, Construction of solutions with exactly k blow-up points for the nonlinear Schroedinger equation with critical non linearity Comm. Math. Phys. 15, 203–254
Sayapova M.R., Yafaev D.R. The evolution operator for time dependent potentials of zero radius, Proc Steklov Inst. Math. 2, 173–180
Teta S. Quadratic forms for singular perturbations of the Laplacean Publ R.I.M.S. 26, 803–817
Yafaev D.R. Scattering theory for time dependent zero-range potentials Ann Inst. H.Poincare 40, 343–359
Yajima K. Existence of solutions for Schroedinger evolution equations, Comm. Math. Phys. 110, 415–426
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© 2000 Springer Science+Business Media Dordrecht
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Dell’Antonio, G. (2000). Moving Point Interactions. In: Spigler, R. (eds) Applied and Industrial Mathematics, Venice—2, 1998. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4193-2_4
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DOI: https://doi.org/10.1007/978-94-011-4193-2_4
Publisher Name: Springer, Dordrecht
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