222 citations · 518 across the 19 of their papers we have counts for
19 papers
Continuous Spectra of Generalized Kronig-Penney Model
Taksu Cheon, T. Shigehara
The standard Kronig-Penney model with periodic potentials is extended to the cases with generalized contact interactions. The eigen equation which determines the dispersion rel…
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
T. Shigehara, H. Mizoguchi, T. Mishima +1
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 w…
Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths
T. Shigehara, H. Mizoguchi, T. Mishima +1
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 th…
Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability
Taksu Cheon, T. Shigehara, K. Takayanagi
We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that…
Some Aspects of Generalized Contact Interaction in One-Dimensional Quantum Mechanics
Taksu Cheon, T. Shigehara
We construct a one-dimensional contact interaction ( potential) which induces the discontinuity of the wave function while keeping its derivative continuous. By combining the $ε…
Influence of Small Impurities on Low-Energy Electron Dynamics in Two-Dimensional Microscopic Bounded Region
T. Shigehara, M. Yokoyama, H. Mizoguchi +2
In order to give some insight into a role of small impurities on the electron motion in microscopic devices, we examine from a general viewpoint, the effect of small obstacles on a…