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T. Mishima

Publications and source records attributed to T. Mishima.

6 recordsLinked to original sources
arXiv1999

Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics

We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $δ$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called $ε$ potential. It will be also shown that the scattering properties at high energy substantially differ between non-relativistic and relativistic cases.

quant-ph↗
arXiv1999

Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths

We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator $T=-Δ\lceil C^{\infty}_{0}({\bf R} \backslash\{0\})$. It is achieved in the small distance limit of equally spaced three neighboring Dirac's $δ$ potentials. The strength for each $δ$ is appropriately renormalized according to the distance and it diverges, in general, in the small distance limit. The validity of our method is ensured by numerical calculations. In general cases except for usual $δ$, the wave function discontinuity appears around the interaction and one can observe such a tendency even at a finite distance level.

quant-ph↗
arXiv1997

Spectral Properties of the Two-Dimensional Laplacian with a Finite Number of Point Interactions

We discuss spectral properties of the Laplacian with multiple ($N$) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a symmetric (Hermitian) operator in functional analysis. The eigenvalues of this system are obtained as the poles of a transition matrix which has size $N$. Closely examining a generic behavior of the eigenvalues of the transition matrix as a function of the energy, we deduce the general condition under which point interactions have a substantial effect on statistical properties of the spectrum.

quant-ph↗