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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 *C*_{0}(**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

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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 *C*_{0}(**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

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@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 *C*_{0}(**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},}

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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 *C*_{0}(**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 -