# 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

**Summary: **

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 *T*_{l=1} of auxilliary operator *T* = ⊕^{∞}_{l=0} *T _{l}* involving the construction of the resolvent for the operator

*H*. In this work together with the previous one two constants 0<

*m*

_{1}<

*m*

_{0}<∞ were found such that: 1) for

*m*>

*m*

_{0}the operator

*T*=1 is selfadjoint but for

_{l}*m*≤

*m*

_{0}it has the deficiency indexes (1, 1); 2) for

*m*

_{1}<

*m*<

*m*

_{0}any selfadjoint extension of

*T*=1 is semibounded from below; 3) for 0<

_{l}*m*<

*m*

_{1}any selfadjoint extension of

*T*=1 has the sequence of eigenvalues {λ

_{l}_{n}<0,

*n*>

*n*

_{0}} with the asymptotics λ

_{n}= λ

_{0}e

^{δn}+

*O*(1), n → ∞, where λ

_{0}<0, δ > 0,

*n*

_{0}>0 and there is no other spectrum on the interval λ<λ

_{n0}.

2010 Mathematics Subject Classification. 81Q10, 47S30.

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

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