Physics – Mathematical Physics
Scientific paper
2005-01-11
Physics
Mathematical Physics
Scientific paper
A model operator $H$ corresponding to a three-particle discrete Schr\"odinger operator on a lattice $\Z^3$ is studied. The essential spectrum is described via the spectrum of two Friedrichs models with parameters $h_\alpha(p),$ $\alpha=1,2,$ $p \in \T^3=(-\pi,\pi]^3.$ The following results are proven: 1) The operator $H$ has a finite number of eigenvalues lying below the bottom of the essential spectrum in any of the following cases: (i) both operators $h_\alpha(0), \alpha=1,2,$ have a zero eigenvalue; (ii) either $h_1(0)$ or $h_2(0)$ has a zero eigenvalue. 2) The operator $H$ has infinitely many eigenvalues lying below the bottom and accumulating at the bottom of the essential spectrum, if both operators $h_\alpha(0),\alpha=1,2,$ have a zero energy resonance.
Albeverio Sergio
Djumanova Ramiza Kh.
Lakaev Saidakhmat N.
No associations
LandOfFree
On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-202013