On contact interactions as limits of short-range potentials. (English) Zbl 1313.81009

Bräunlich, Gerhard; Hainzl, Christian; Seiringer, Robert

Methods Funct. Anal. Topol. 19, No. 4, 364-375 (2013).

The physical applications of Hamiltonians of point interactions defined as extensions of operators require a correct choice of the extension. In particular, in models of cold atomic gases the choice is based on approximation by short-range potentials \(V_l\) with the range \(l\) converging to zero, as \(l\to 0\), while the scattering length tends to a finite limit. The paper provides a rigorous implementation of the above idea. The interaction \(V_l\) is required to have a strong repusive core. An important ingredient is a formula for the scattering length obtained by C. Hainzl and R. Seiringer [Lett. Math. Phys. 84, No. 2-3, 99–107 (2008; Zbl 1164.81006)].

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis
35Q40	PDEs in connection with quantum mechanics
47N50	Applications of operator theory in the physical sciences

Keywords:

contact interaction; short-range potential; scattering length

Citations:

Zbl 1164.81006