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Bound States of a System of Two Fermions on Invariant Subspace
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作者 J. I. abdullaev a. m. toshturdiev 《Journal of Modern Physics》 2021年第1期35-49,共15页
We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z<sup>3</sup> with special potential <img alt="" src="Edit_56564354-6d65-4104-9126-d4657fa750af.png&qu... We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z<sup>3</sup> with special potential <img alt="" src="Edit_56564354-6d65-4104-9126-d4657fa750af.png" />. The corresponding Shr&ouml;dinger operator <em>H</em>(<strong>k</strong>) of the system has an invariant subspac <span style="white-space:nowrap;"><span><em>L</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub>(T<sup>3</sup>)</span> , where we study the eigenvalues and eigenfunctions of its restriction <span style="white-space:nowrap;"><span><em>H</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub></span><span style="white-space:nowrap;">(<strong>k</strong>)</span>. Moreover, there are shown that <span style="white-space:nowrap;"><span><em>H</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub>(<em>k</em><sub>1</sub>, <em>k</em><sub>2</sub>, π)</span> has also infinitely many invariant subspaces <img alt="" src="Edit_4955ffad-4b18-434a-8c99-ff14779f2812.bmp" />, where the eigenvalues and eigenfunctions of eigenvalue problem <img alt="" src="Edit_01b218d2-fa3e-4f39-bc2d-ce736205db93.bmp" />are explicitly found. 展开更多
关键词 HAMILTONIAN FERMION Bound State Shrödinger Operator Invariant Subspace Total Quasi-Momentum Eigenvalue Birman-Schwinger Principle
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