zbMATH — the first resource for mathematics

The Efimov effect of three-body Schrödinger operators. (English) Zbl 0761.35078
The author considers three-body Schrödinger operators, with pair potentials decaying at infinity like \(| x|^{-\rho}\) with \(\rho>2\).
Assuming that all two-particles subsystems have no negative bound states but a zero resonance energy, it is proved that the whole system has an infinite number of negative bound states energies, accumulating at zero (Efimov effect).

35P25 Scattering theory for PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
81U10 \(n\)-body potential quantum scattering theory
35Q40 PDEs in connection with quantum mechanics
Full Text: DOI
[1] Efimov, V, Energy levels arising from resonant two-body forces in a three-body system, Phys. lett. B, 33, 563-564, (1970)
[2] Jensen, A; Kato, T, Spectral properties of Schrödinger operators and time-decay of the wave functions, Duke math. J., 46, 583-611, (1979) · Zbl 0448.35080
[3] Kirsch, W; Simon, B, Corrections to the classical behavior of the number of bound states of Schrödinger operators, Ann. physics, 183, 122-130, (1988) · Zbl 0646.35019
[4] Klaus, M; Simon, B, Binding of Schrödinger particles through conspiracy of potential wells, Ann. inst. H. Poincaré, sect. A, 30, 83-87, (1979)
[5] Murata, M, Asymptotic expansion in time for solutions of Schrödinger type equations, J. funct. anal., 49, 10-56, (1982) · Zbl 0499.35019
[6] Newton, R.G, Scattering theory of waves and particles, (1982), Springer-Verlag New York/Heidelberg/Berlin · Zbl 0496.47011
[7] Ovchinnikov, Yu.N; Sigal, I.M, Number of bound states of three-body systems and Efimov’s effect, Ann. physics, 123, 274-295, (1979)
[8] Yafaev, D.R, On the theory of the discrete spectrum of the three-particle Schrödinger operator, Math. USSR-sb., 23, 535-559, (1974) · Zbl 0342.35041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.