An application of bilinear integration to quantum scattering

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• 作者：L.M. Garcí ; a-Raffi^a ; ¹ ; ^{lmgarcia@mat.upv.es" class="auth_mail} ; B. Jefferies^b ; ² ; ^{b.jefferies@unsw.edu.au" class="auth_mail}
• 关键词：Scattering theory ; Time-dependent ; Stationary theory ; Bilinear integration ; Tensor products
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：1 July, 2014
• 年：2014
• 卷：415
• 期：1
• 页码：394-421
• 全文大小：429 K

文摘

Scattering theory has its origin in Quantum Mechanics. From the mathematical point of view it can be considered as a part of perturbation theory of self-adjoint operators on the absolutely continuous spectrum. In this work we deal with the passage from the time-dependent formalism to the stationary state scattering theory. This problem involves applying Fubini's Theorem to a spectral measure integral and a Lebesgue integral of functions that take values in spaces of operators. In our approach, we use bilinear integration in a tensor product of spaces of operators with suitable topologies and generalize the results previously stated in the literature.