Hideo Tamura

The Efimov effect of three-body Schrödinger operators

Abstract The author studies the Efimov effect of three-body Schrodinger operators. By use of the variational method, the effect is proved under the assumptions that pair potentials fall off with order O(¦x¦ −ϱ ), ϱ > 2 , at infinity and that all three two-body subsystems have a zero resonance energy.

Error estimate in operator norm for Trotter-Kato product formula

In the present paper we study the error estimate in the operator norm for the Trotter-Kato product formula, having an intention to apply the obtained result to Schrödinger semigroups with singular potentials.

Asymptotic completeness for long-range many-particle systems with Stark effect. II

We prove the existence and the asymptotic completeness of the Dollard-type modified wave operators for many-particle Stark Hamiltonians with long-range potentials.

Semi-classical limit of scattering length

For scattering by a finite range potential, it is shown that the scattering length is convergent to the capacity of the support of the finite range potential in the semi-classical limit. This result has been already proved by use of probabilistic methods. Here we give an alternative proof without using any probabilistic idea. The proof is purely analytical and very simple.

On the norm convergence of the self-adjoint Trotter-Kato product formula with error bound

The norm convergence of the Trotter—Kato product formula with error bound is shown for the semigroup generated by that operator sum of two nonnegative self-adjoint operatorsA andB which is self-adjoint.