INVESTIGATION OF QUANTUM WAVEGUIDES (SOLUTION OF HELMHOLTZ’S EQUATION AT ANY ARBITRARY CROSS SECTIONAL AREA)

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TABATABAEIFAR A.H.; IZADNESHAN H.

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Journal: JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY) Year:2010 | Volume:20 | Issue:75 (PHYSICS ISSUE) Page(s): 129-139

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Title

INVESTIGATION OF QUANTUM WAVEGUIDES (SOLUTION OF HELMHOLTZ’S EQUATION AT ANY ARBITRARY CROSS SECTIONAL AREA)

Author(s)

TABATABAEIFAR A.H. | IZADNESHAN H. | Issue Writer Certificate

Keywords

BILLIARDQ3

QUANTUM WAVEGUIDEQ3

HELMHOLTZ’S EQUATIONQ3

HELLER METHODSQ3

Abstract

Introduction: Nowadays extraordinary properties of nano world and economical problems are the reasons for directing techniques toward micro implements, electronic circuits dimensions have been reduced to 10 to 100 nano meters. Moreover microstructures in cells with nano meter dimensions have been investigated by biologists, there are structures in electronic and biology which are very similar to the BILLIARDs and the electromagnetic waveguides but their dimensions are in nano meter range, therefore they were called QUANTUM WAVEGUIDEs and BILLIARDs.Aim: In this research BILLIARDs and QUANTUM WAVEGUIDEs at any arbitrary cross sectional area have been investigated.Method: A considerable effort was devoted in solving HELMHOLTZ’S EQUATION with two dimensional cross sectional areas. Linear combinations of plane waves or HELLER METHODS for several types of connective and no connective BILLIARDs with regular and irregular shapes have been used. Then eigenvalues and eigenvectors were calculated. At the final part by applying a simple method BILLIARD type (chaotic or quiet) in a quantum scale has been realized.Results and Discussions: In this paper two types of circular and stadium BILLIARDs have been studied and by using Heller’s method and applying the numerical solution, energy levels together with the function forms have been attained.Conclusions: This paper shows that Heller’s method despite its quickness and simplicity is a very accurate method for finding eigenvalues and eigenvectors. Although in high eigenvalues the calculation is weighted, nevertheless this method is an acceptable computational method for the investigation of quantum nanoBILLIARDs such as quantum points.

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APA: Copy

TABATABAEIFAR, A.H., & IZADNESHAN, H.. (2010). INVESTIGATION OF QUANTUM WAVEGUIDES (SOLUTION OF HELMHOLTZ’S EQUATION AT ANY ARBITRARY CROSS SECTIONAL AREA). JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY), 20(75 (PHYSICS ISSUE)), 129-139. SID. https://sid.ir/paper/70512/en

Vancouver: Copy

TABATABAEIFAR A.H., IZADNESHAN H.. INVESTIGATION OF QUANTUM WAVEGUIDES (SOLUTION OF HELMHOLTZ’S EQUATION AT ANY ARBITRARY CROSS SECTIONAL AREA). JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY)[Internet]. 2010;20(75 (PHYSICS ISSUE)):129-139. Available from: https://sid.ir/paper/70512/en

IEEE: Copy

A.H. TABATABAEIFAR, and H. IZADNESHAN, “INVESTIGATION OF QUANTUM WAVEGUIDES (SOLUTION OF HELMHOLTZ’S EQUATION AT ANY ARBITRARY CROSS SECTIONAL AREA),” JOURNAL OF SCIENCES (ISLAMIC AZAD UNIVERSITY), vol. 20, no. 75 (PHYSICS ISSUE), pp. 129–139, 2010, [Online]. Available: https://sid.ir/paper/70512/en

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