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Moscow Mathematical Journal

Volume 14, Issue 3, July–September 2014  pp. 617–637.

On Point-Like Interaction of Three Particles: Two Fermions and Another Particle. II

Authors:  R.A. Minlos (1)
Author institution:(1) Institute for Information Transmission Problems of Russian Academy of Sciences, Bolshoy Karetnyi 19, Moscow, Russia


This work continues our previous article, where the construction of Hamiltonian H for the system of three quantum particles is considered. Namely the system consists of two fermions with mass 1 and another particle with mass m>0. In the present paper, like before, we study the part Tl=1 of auxilliary operator T = ⊕l=0 Tl involving the construction of the resolvent for the operator H. In this work together with the previous one two constants 0<m1<m0<∞ were found such that: 1) for m>m0 the operator Tl=1 is selfadjoint but for mm0 it has the deficiency indexes (1, 1); 2) for m1<m<m0 any selfadjoint extension of Tl=1 is semibounded from below; 3) for 0<m<m1 any selfadjoint extension of Tl=1 has the sequence of eigenvalues {λn<0, n>n0} with the asymptotics λn = λ0 eδn + O(1), n → ∞, where λ0<0, δ > 0, n0>0 and there is no other spectrum on the interval λ<λn0.

2010 Mathematics Subject Classification. 81Q10, 47S30.

Keywords: Selfadjoint extension, Mellin’s transformation, formula of Sokhotsky, boundedness from below, deficincy index.

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