Asymptotic Completeness of Long-Range N-Body Quantum Systems

On the Mourre Estimates for Three Body Schroedinger Operators in a Constant Magnetic Field

“…By virtue of this family fk a ð y a max Þg a A Anfð2; 3Þg , one can determine the nearest center of charge for the neutral particle among y 2 , y 3 and y cc : We define a family of sets fW a g a A Anfð2; 3Þg as where r aða min Þ 1 0. The following proposition is proved in the way quite similar to that in [15], [7] and [8]. …”

Tosio Kato’s work on non-relativistic quantum mechanics: part 2

“…We note that the earliest proofs of N -body asymptotic completeness for 0(|x| −1− ) potentials (at least when N ≥ 4) were by Sigal-Soffer [564,565] and then by Graf [196] and Dereziński [115]. Dereziński [115] and Sigal and Soffer [565] have results on long range results.…”

“…Dereziński [115] and Sigal and Soffer [565] have results on long range results. In [700], Yafaev found a proof that exploits smoothness ideas (as well as some of the tools-Mourre estimates [177,448,482], Deift-Simon wave operators [110], Enss type phase space analysis [139,140]-of the earlier approaches).…”

On the Energy-Momentum Spectrum of a Homogeneous Fermi Gas

“…One can show that these systems are asymptotically complete (see [10] and references therein). In this case the system is invariant wrt.…”