Scattering theory for quasi-one-dimensional tunneling structures

A. M. Kriman; D. K. Ferry

doi:10.1016/0749-6036(87)90232-1

Scattering theory for quasi-one-dimensional tunneling structures

A. M. Kriman, D. K. Ferry

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Quantum theoretical studies of semiconductor microstructures are most naturally done in terms of one-dimensional scattering states, which are characterized far from a structure by k-dependent reflection and transmission amplitudes. We have investigated these states using integral forms such as the Lippmann-Schwinger equation. These allow us to obtain global properties of the states and provide the basis for a formal scattering theory of the kind that has been developed for the conventional problem of three-dimensional potential scattering. We find orthonormality relations for the scattering states, the one-dimensional analogues of Wigner's inequality and Levinson's theorem, and associated properties of the complex-momentum transmission amplitude.

Original language	English (US)
Pages (from-to)	503-507
Number of pages	5
Journal	Superlattices and Microstructures
Volume	3
Issue number	5
DOIs	https://doi.org/10.1016/0749-6036(87)90232-1
State	Published - 1987

ASJC Scopus subject areas

General Materials Science
Condensed Matter Physics
Electrical and Electronic Engineering

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10.1016/0749-6036(87)90232-1

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title = "Scattering theory for quasi-one-dimensional tunneling structures",

abstract = "Quantum theoretical studies of semiconductor microstructures are most naturally done in terms of one-dimensional scattering states, which are characterized far from a structure by k-dependent reflection and transmission amplitudes. We have investigated these states using integral forms such as the Lippmann-Schwinger equation. These allow us to obtain global properties of the states and provide the basis for a formal scattering theory of the kind that has been developed for the conventional problem of three-dimensional potential scattering. We find orthonormality relations for the scattering states, the one-dimensional analogues of Wigner's inequality and Levinson's theorem, and associated properties of the complex-momentum transmission amplitude.",

author = "Kriman, {A. M.} and Ferry, {D. K.}",

note = "Funding Information: Acknovledgnent - The authors would like thank N. Teranishi for useful discussions. This work was supported in part by the Office of Naval Research.",

year = "1987",

doi = "10.1016/0749-6036(87)90232-1",

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T1 - Scattering theory for quasi-one-dimensional tunneling structures

AU - Kriman, A. M.

AU - Ferry, D. K.

N1 - Funding Information: Acknovledgnent - The authors would like thank N. Teranishi for useful discussions. This work was supported in part by the Office of Naval Research.

PY - 1987

Y1 - 1987

N2 - Quantum theoretical studies of semiconductor microstructures are most naturally done in terms of one-dimensional scattering states, which are characterized far from a structure by k-dependent reflection and transmission amplitudes. We have investigated these states using integral forms such as the Lippmann-Schwinger equation. These allow us to obtain global properties of the states and provide the basis for a formal scattering theory of the kind that has been developed for the conventional problem of three-dimensional potential scattering. We find orthonormality relations for the scattering states, the one-dimensional analogues of Wigner's inequality and Levinson's theorem, and associated properties of the complex-momentum transmission amplitude.

AB - Quantum theoretical studies of semiconductor microstructures are most naturally done in terms of one-dimensional scattering states, which are characterized far from a structure by k-dependent reflection and transmission amplitudes. We have investigated these states using integral forms such as the Lippmann-Schwinger equation. These allow us to obtain global properties of the states and provide the basis for a formal scattering theory of the kind that has been developed for the conventional problem of three-dimensional potential scattering. We find orthonormality relations for the scattering states, the one-dimensional analogues of Wigner's inequality and Levinson's theorem, and associated properties of the complex-momentum transmission amplitude.

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ER -

Scattering theory for quasi-one-dimensional tunneling structures

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