On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Sch...
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| Main Authors: | , |
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| Format: | Article |
| Published: |
Allerton Press Incorporation
2016
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/70094/ http://dx.doi.org/10.3103/S1066369X16010035 |
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| Summary: | On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case, when potentials satisfy some conditions and zero is a regular point for two-particle sub-Hamiltonian. We find a set of values for particles masses values such that Schrödinger operator may have only finite number of eigenvalues lying to the left of essential spectrum. |
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