THE ESSENTIAL SPECTRUM OF THE SCHRÖDINGER OPERATOR FOR A THREE-PARTICLE SYSTEM WITH MASSES m1 = M2 = c∞ AND m3 < ∞

Muminov, Zahriddin

Innovations in Science and Technologies Том 2 № 6 (2025) · с. 678-687

THE ESSENTIAL SPECTRUM OF THE SCHRÖDINGER OPERATOR FOR A THREE-PARTICLE SYSTEM WITH MASSES m1 = M2 = c∞ AND m3 < ∞

Muminov, Zahriddin

Аннотация

We consider a family of parameter-dependent discrete Schrödinger operators corresponding to the Hamiltonian ofa system of three arbitrary particles (either fermions or bosons) with masses m₁ = m₂ = ∞ and m3 <o, on the integer lattice, Z3. The interactions ofparticles are describedvia zero-range attractive forces. Using the direct-integral decomposition method, the threeparticle problem is reduced to the study of simpler two-particle Schrödinger operators, called the channel (or fiber) operators. Using the channel operators, wefind that the essential spectrum consists of a finite union of real segments.

Schrödinger operator, spectrum, essential spectrum, Fredholm determinant.

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