Derivation of tunneling probabilities for arbitrarily graded potential barriers using modified Airy functions

Kyu Tae Lee; Eun Joo Jung; Chul Han Kim; Chang Min Kim

doi:10.1007/s11082-010-9434-7

Derivation of tunneling probabilities for arbitrarily graded potential barriers using modified Airy functions

Kyu Tae Lee, Eun Joo Jung, Chul Han Kim, Chang Min Kim

School of Electrical and Computer Engineering

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

1 Scopus citations

Abstract

General expressions of tunneling probability for arbitrarily graded potential barriers are rigorously derived using the modified Airy functions. Three types of graded potential barriers for which exact solutions exist are taken as examples for comparison's purpose. Results obtained by the proposed method are confirmed to be in fairly good agreement with exact ones, demonstrating the usefulness of the modified Airy functions method.

Original language	English
Pages (from-to)	129-141
Number of pages	13
Journal	Optical and Quantum Electronics
Volume	42
Issue number	2
DOIs	https://doi.org/10.1007/s11082-010-9434-7
State	Published - Jan 2010

Keywords

Graded potential barrier
Modified Airy functions
Tunneling probability
WKB method

Access to Document

10.1007/s11082-010-9434-7

Cite this

@article{28103fb667a74ec781dc04c80625937b,

title = "Derivation of tunneling probabilities for arbitrarily graded potential barriers using modified Airy functions",

abstract = "General expressions of tunneling probability for arbitrarily graded potential barriers are rigorously derived using the modified Airy functions. Three types of graded potential barriers for which exact solutions exist are taken as examples for comparison's purpose. Results obtained by the proposed method are confirmed to be in fairly good agreement with exact ones, demonstrating the usefulness of the modified Airy functions method.",

keywords = "Graded potential barrier, Modified Airy functions, Tunneling probability, WKB method",

author = "Lee, {Kyu Tae} and Jung, {Eun Joo} and Kim, {Chul Han} and Kim, {Chang Min}",

year = "2010",

month = jan,

doi = "10.1007/s11082-010-9434-7",

language = "English",

volume = "42",

pages = "129--141",

journal = "Optical and Quantum Electronics",

issn = "0306-8919",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Derivation of tunneling probabilities for arbitrarily graded potential barriers using modified Airy functions

AU - Lee, Kyu Tae

AU - Jung, Eun Joo

AU - Kim, Chul Han

AU - Kim, Chang Min

PY - 2010/1

Y1 - 2010/1

N2 - General expressions of tunneling probability for arbitrarily graded potential barriers are rigorously derived using the modified Airy functions. Three types of graded potential barriers for which exact solutions exist are taken as examples for comparison's purpose. Results obtained by the proposed method are confirmed to be in fairly good agreement with exact ones, demonstrating the usefulness of the modified Airy functions method.

AB - General expressions of tunneling probability for arbitrarily graded potential barriers are rigorously derived using the modified Airy functions. Three types of graded potential barriers for which exact solutions exist are taken as examples for comparison's purpose. Results obtained by the proposed method are confirmed to be in fairly good agreement with exact ones, demonstrating the usefulness of the modified Airy functions method.

KW - Graded potential barrier

KW - Modified Airy functions

KW - Tunneling probability

KW - WKB method

UR - http://www.scopus.com/inward/record.url?scp=79951721604&partnerID=8YFLogxK

U2 - 10.1007/s11082-010-9434-7

DO - 10.1007/s11082-010-9434-7

M3 - Article

AN - SCOPUS:79951721604

SN - 0306-8919

VL - 42

SP - 129

EP - 141

JO - Optical and Quantum Electronics

JF - Optical and Quantum Electronics

IS - 2

ER -

Derivation of tunneling probabilities for arbitrarily graded potential barriers using modified Airy functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this