Matches in SemOpenAlex for { <https://semopenalex.org/work/W4385300372> ?p ?o ?g. }
Showing items 1 to 73 of
73
with 100 items per page.
- W4385300372 endingPage "107" @default.
- W4385300372 startingPage "61" @default.
- W4385300372 abstract "In this chapter, we first describe the scattering phenomenon from the mathematical viewpoint and introduce wave operator and S-matrix. Improving the Mourre theory to allow singularities for the potential, we then discuss the asymptotic completeness of wave operators for a system composed of two particles. Three methods are explained: (1) The theory of smooth perturbation; (2) Enss’ time-dependent method; (3) Commutator calculus and Heisenberg derivatives. The method (1) entails a series of inqualities based on fundamental relations between the resolvent and the unitary group of a self-adjoint operator. The method (2) deals with only the unitary group and is based on the intuition that quantum mechanical particles in a scattering state move asymptotically along the orbit in classical mechanics. The method (3) is based on the same picture and employs commutation relations of quantum mechanical observables which have counterparts in classical mechanics. All of these ideas are used in the later arguments. The assumption for the two-body potential V(x) is as follows. V(x) is split as $$V(x) = V_0(x) + V_S(x) + V_L(x)$$ and satisfies the following conditions: 2.1 $$begin{aligned} left{ begin{aligned}&(V{text{- }}0) langle xrangle ^2V_0(x) in L^p(textbf{R}^n), text {where} p = 2 (n le 3), p > n/2 (n ge 4),&(V{text{- }}S) |V_S(x)| le Clangle xrangle ^{-1-rho } (0 < rho le 1), &(V{text{- }}L) |partial ^{alpha }V_L(x)| le Clangle xrangle ^{-|alpha |-rho } (|alpha | le 1). end{aligned} right. end{aligned}$$ We prove the limiting absorption principle for H, which is closely related to the smooth perturbation theory. In the Heisenberg derivative method, we do not use the whole Mourre theory but only the Mourre inequality." @default.
- W4385300372 created "2023-07-28" @default.
- W4385300372 creator A5084765499 @default.
- W4385300372 date "2023-01-01" @default.
- W4385300372 modified "2023-09-25" @default.
- W4385300372 title "Two-Body Problem" @default.
- W4385300372 cites W1552513371 @default.
- W4385300372 cites W1569024867 @default.
- W4385300372 cites W1983659462 @default.
- W4385300372 cites W1989567861 @default.
- W4385300372 cites W2012070244 @default.
- W4385300372 cites W2025147649 @default.
- W4385300372 cites W2043618567 @default.
- W4385300372 cites W2092456331 @default.
- W4385300372 cites W2317453708 @default.
- W4385300372 cites W4239484867 @default.
- W4385300372 cites W4298653657 @default.
- W4385300372 doi "https://doi.org/10.1007/978-981-99-3704-2_2" @default.
- W4385300372 hasPublicationYear "2023" @default.
- W4385300372 type Work @default.
- W4385300372 citedByCount "0" @default.
- W4385300372 crossrefType "book-chapter" @default.
- W4385300372 hasAuthorship W4385300372A5084765499 @default.
- W4385300372 hasConcept C104317684 @default.
- W4385300372 hasConcept C121332964 @default.
- W4385300372 hasConcept C145620117 @default.
- W4385300372 hasConcept C158448853 @default.
- W4385300372 hasConcept C161094330 @default.
- W4385300372 hasConcept C17020691 @default.
- W4385300372 hasConcept C185592680 @default.
- W4385300372 hasConcept C191486275 @default.
- W4385300372 hasConcept C32848918 @default.
- W4385300372 hasConcept C33923547 @default.
- W4385300372 hasConcept C37914503 @default.
- W4385300372 hasConcept C51568863 @default.
- W4385300372 hasConcept C55493867 @default.
- W4385300372 hasConcept C62520636 @default.
- W4385300372 hasConcept C73648015 @default.
- W4385300372 hasConcept C86339819 @default.
- W4385300372 hasConceptScore W4385300372C104317684 @default.
- W4385300372 hasConceptScore W4385300372C121332964 @default.
- W4385300372 hasConceptScore W4385300372C145620117 @default.
- W4385300372 hasConceptScore W4385300372C158448853 @default.
- W4385300372 hasConceptScore W4385300372C161094330 @default.
- W4385300372 hasConceptScore W4385300372C17020691 @default.
- W4385300372 hasConceptScore W4385300372C185592680 @default.
- W4385300372 hasConceptScore W4385300372C191486275 @default.
- W4385300372 hasConceptScore W4385300372C32848918 @default.
- W4385300372 hasConceptScore W4385300372C33923547 @default.
- W4385300372 hasConceptScore W4385300372C37914503 @default.
- W4385300372 hasConceptScore W4385300372C51568863 @default.
- W4385300372 hasConceptScore W4385300372C55493867 @default.
- W4385300372 hasConceptScore W4385300372C62520636 @default.
- W4385300372 hasConceptScore W4385300372C73648015 @default.
- W4385300372 hasConceptScore W4385300372C86339819 @default.
- W4385300372 hasLocation W43853003721 @default.
- W4385300372 hasOpenAccess W4385300372 @default.
- W4385300372 hasPrimaryLocation W43853003721 @default.
- W4385300372 hasRelatedWork W1500656620 @default.
- W4385300372 hasRelatedWork W1532953111 @default.
- W4385300372 hasRelatedWork W165780274 @default.
- W4385300372 hasRelatedWork W2048963143 @default.
- W4385300372 hasRelatedWork W2057478972 @default.
- W4385300372 hasRelatedWork W2105572611 @default.
- W4385300372 hasRelatedWork W2371181305 @default.
- W4385300372 hasRelatedWork W2371512749 @default.
- W4385300372 hasRelatedWork W2470947461 @default.
- W4385300372 hasRelatedWork W3030132518 @default.
- W4385300372 isParatext "false" @default.
- W4385300372 isRetracted "false" @default.
- W4385300372 workType "book-chapter" @default.