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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| Format: | Article |
| Language: | English |
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University of South Florida
2010-01-01
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| Series: | Undergraduate Journal of Mathematical Modeling: One + Two |
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| Online Access: | http://scholarcommons.usf.edu/ujmm/vol2/iss2/6 |
| _version_ | 1818248131772416000 |
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| author | Tim Mitchell |
| author_facet | Tim Mitchell |
| author_sort | Tim Mitchell |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-12T15:15:44Z |
| format | Article |
| id | doaj.art-74ab161cc3164cc783b357f5cbbfb213 |
| institution | Directory Open Access Journal |
| issn | 2326-3652 |
| language | English |
| last_indexed | 2024-12-12T15:15:44Z |
| publishDate | 2010-01-01 |
| publisher | University of South Florida |
| record_format | Article |
| series | Undergraduate Journal of Mathematical Modeling: One + Two |
| spelling | doaj.art-74ab161cc3164cc783b357f5cbbfb2132022-12-22T00:20:30ZengUniversity 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 |
| spellingShingle | Tim Mitchell Quantum Mechanical Example of Anti-Tunneling Undergraduate Journal of Mathematical Modeling: One + Two Quantam Anti Tunneling, Schrodinger’s Equation, Reflection Coefficient |
| title | 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_short | Quantum Mechanical Example of Anti-Tunneling |
| title_sort | quantum mechanical example of anti tunneling |
| 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 |