Abstract
We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z3 with special potential . The corresponding Shrödinger operator H(k) of the system has an invariant subspac L-123(T3) , where we study the eigenvalues and eigenfunctions of its restriction H-123(k). Moreover, there are shown that H-123(k1, k2, π) has also infinitely many invariant subspaces , where the eigenvalues and eigenfunctions of eigenvalue problem are explicitly found.
Highlights
The nature of bound states of two-particle cluster operators for small parameter values was first studied in detail by Minlos and Mamatov [1] and in a more general setting by Minlos and Mogilner [2]
( ) H (k ) of the system has an invariant subspace L1−23 3, where we study the eigenvalues and eigenfunctions of its restriction H1−23 (k )
In [3], Howland showed that the Rellich theorem on perturbations of eigenvalues does not extend to the resonance theory
Summary
The nature of bound states of two-particle cluster operators for small parameter values was first studied in detail by Minlos and Mamatov [1] and in a more general setting by Minlos and Mogilner [2]. Studying bound states of a two-particle system Hamiltonian H on the d-dimensional lattice d reduces to studying [2] [4] [5] [6] [7] the eigenvalues of a family of Shrödinger operators H (k ),k ∈ d , where k is the total quasi-momentum of a system. Shrödinger operator on a one-dimensional lattice were studied in [8]. The finiteness of the number of eigenvalues of Shrödinger operator on a lattice was studied in the works [7] [9]. H (π − 2β ,π − 2β ,π ) f = zf , f ∈ R1−23 (n) with small β are solved by using methods invariant subspaces and operator theory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
