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

Takaomi SHIGEHARA; Hiroshi MIZOGUCHI; Taketoshi MISHIMA; Taksu CHEON

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

Takaomi SHIGEHARA, Hiroshi MIZOGUCHI, Taketoshi MISHIMA, Taksu CHEON

Full Text Views

0

Cite this

Summary :

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 C₀(R \{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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.9 pp.1708-1713

Publication Date: 1999/09/25

Publicized

Online ISSN

DOI

Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)

Category

Cite this

Copy

Takaomi SHIGEHARA, Hiroshi MIZOGUCHI, Taketoshi MISHIMA, Taksu CHEON, "Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths" in IEICE TRANSACTIONS on Fundamentals, vol. E82-A, no. 9, pp. 1708-1713, September 1999, doi: .
Abstract: 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 C₀(R \{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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_9_1708/_p

Copy

@ARTICLE{e82-a_9_1708,
author={Takaomi SHIGEHARA, Hiroshi MIZOGUCHI, Taketoshi MISHIMA, Taksu CHEON, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths},
year={1999},
volume={E82-A},
number={9},
pages={1708-1713},
abstract={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 C₀(R \{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.},
keywords={},
doi={},
ISSN={},
month={September},}

Copy

TY - JOUR
TI - Realization of a Four Parameter Family of Generalized One-Dimensional Contact Interactions by Three Nearby Delta Potentials with Renormalized Strengths
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1708
EP - 1713
AU - Takaomi SHIGEHARA
AU - Hiroshi MIZOGUCHI
AU - Taketoshi MISHIMA
AU - Taksu CHEON
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1999
AB - 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 C₀(R \{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.
ER -