Quantum Mechanical Example of Anti-Tunneling

The probability of a particle being reflected by a semi-infinite energy barrier was solved using Schrödinger's equations that describe the quantum mechanical behavior of the particle. The continuity of the functions at the origin allowed the wave functions and their respective derivati...

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Main Author:	Tim Mitchell
Format:	Article
Language:	English
Published:	University of South Florida 2010-01-01
Series:	Undergraduate Journal of Mathematical Modeling: One + Two
Subjects:	Quantam Anti Tunneling, Schrodinger’s Equation, Reflection Coefficient
Online Access:	http://scholarcommons.usf.edu/ujmm/vol2/iss2/6

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spelling	doaj-74ab161cc3164cc783b357f5cbbfb2132020-11-24T22:43:26ZengUniversity of South FloridaUndergraduate Journal of Mathematical Modeling: One + Two2326-36522010-01-012210.5038/2326-3652.2.2.6Quantum Mechanical Example of Anti-TunnelingTim MitchellThe probability of a particle being reflected by a semi-infinite energy barrier was solved using Schrödinger's equations that describe the quantum mechanical behavior of the particle. The continuity of the functions at the origin allowed the wave functions and their respective derivatives to be equated. Solution of the resulting system yielded values A<sub>1</sub> and B<sub>1</sub> which were used to calculate the reflection coefficient, (B<sub>1</sub>/A<sub>1</sub>)<sup>2</sup>. The conclusions obtained from these results stated that the particle would be reflected by the barrier when E<V. The probability of the particle being reflected decreased exponentially as the E/V ratio increased.http://scholarcommons.usf.edu/ujmm/vol2/iss2/6Quantam Anti Tunneling, Schrodinger’s Equation, Reflection Coefficient
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tim Mitchell
spellingShingle	Tim Mitchell Quantum Mechanical Example of Anti-Tunneling Undergraduate Journal of Mathematical Modeling: One + Two Quantam Anti Tunneling, Schrodinger’s Equation, Reflection Coefficient
author_facet	Tim Mitchell
author_sort	Tim Mitchell
title	Quantum Mechanical Example of Anti-Tunneling
title_short	Quantum Mechanical Example of Anti-Tunneling
title_full	Quantum Mechanical Example of Anti-Tunneling
title_fullStr	Quantum Mechanical Example of Anti-Tunneling
title_full_unstemmed	Quantum Mechanical Example of Anti-Tunneling
title_sort	quantum mechanical example of anti-tunneling
publisher	University of South Florida
series	Undergraduate Journal of Mathematical Modeling: One + Two
issn	2326-3652
publishDate	2010-01-01
description	The probability of a particle being reflected by a semi-infinite energy barrier was solved using Schrödinger's equations that describe the quantum mechanical behavior of the particle. The continuity of the functions at the origin allowed the wave functions and their respective derivatives to be equated. Solution of the resulting system yielded values A<sub>1</sub> and B<sub>1</sub> which were used to calculate the reflection coefficient, (B<sub>1</sub>/A<sub>1</sub>)<sup>2</sup>. The conclusions obtained from these results stated that the particle would be reflected by the barrier when E<V. The probability of the particle being reflected decreased exponentially as the E/V ratio increased.
topic	Quantam Anti Tunneling, Schrodinger’s Equation, Reflection Coefficient
url	http://scholarcommons.usf.edu/ujmm/vol2/iss2/6
work_keys_str_mv	AT timmitchell quantummechanicalexampleofantitunneling
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Quantum Mechanical Example of Anti-Tunneling

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