Towards the Analytical Generalization of the Transcendental Energy Equation, Group Velocity, and Effective Mass in One-Dimensional Periodic Potential Wells with a Computational Application to Common Coupled Potentials
Abstract
:Featured Application
Abstract
1. Introduction
2. Theoretical Model Background and Simulation Details
3. Results
3.1. Periodic Potential of One Potential and a Rectangular-like Barrier
3.1.1. Rectangular-like Potential of Negative Intensity
3.1.2. Linear Potential with a Positive Slope
3.1.3. Linear Potential with a Negative Slope
3.2. Group Velocity and Effective Mass for Rectangular-like Potentials of Negative Intensities
Group Velocity and Effective Mass for Linear Potentials
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1
Appendix A.2
Appendix A.3
Appendix A.4
Appendix A.5
Appendix A.6
Appendix B
Group Velocity | a | b | |||
---|---|---|---|---|---|
100 | 1/10 | 1/2 | 1.23 | −6.08 | |
100 | 1/10 | 1/2 | 1.93 | 11.5 | |
Effective Mass | |||||
100 | 1/10 | 1/2 | 1.22 | 13.5 | |
100 | 1/10 | 1/2 | 1.92 | 40.5 |
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First Energy Band | a | w | b | |
---|---|---|---|---|
positive | 100 | 1/10 | 125 | 1/2 |
100 | 1/10 | 25 | 1/2 | |
75 | 1/10 | 5 | 1/3 | |
75 | 1/10 | 5/2 | 1/3 | |
50 | 1/5 | 25 | 1/2 | |
50 | 1/5 | 150 | 1/2 | |
150 | 1/10 | 30 | 1/2 | |
150 | 1/10 | 150 | 1/2 | |
150 | 1/5 | 100 | 1/3 | |
150 | 1/5 | 120 | 1/3 | |
negative | 100 | 1/10 | 100 | 1/2 |
100 | 1/10 | 10 | 1/2 | |
75 | 1/10 | 10 | 1/3 | |
75 | 1/10 | 25 | 1/3 | |
50 | 1/5 | 10 | 1/2 | |
50 | 1/5 | 100 | 1/2 | |
150 | 1/10 | 20 | 1/2 | |
150 | 1/10 | 100 | 1/2 | |
150 | 1/5 | 20 | 1/3 | |
150 | 1/5 | 30 | 1/3 |
Group Velocity | w | ||
---|---|---|---|
Positive slope linear potential | 100 | 1.62 | 0.01550 |
75 | 1.62 | 0.00835 | |
50 | 1.62 | 0.00456 | |
25 | 1.62 | 0.00257 | |
10 | 1.62 | 0.00192 | |
Negative slope linear potential | 100 | 1.62 | 0.003110 |
75 | 1.62 | 0.001920 | |
50 | 1.62 | 0.001160 | |
25 | 1.62 | 0.000701 | |
10 | 1.62 | 0.000544 |
Effective Mass | w | E | |
---|---|---|---|
Positive slope linear potential | 100 | 1.57 | 62.2 |
75 | 1.57 | 52.5 | |
50 | 1.57 | 41.9 | |
25 | 1.57 | 30.2 | |
10 | 1.58 | 22.1 | |
Negative slope linear potential | 100 | 1.57 | 59.4 |
75 | 1.57 | 49.9 | |
50 | 1.57 | 39.3 | |
25 | 1.57 | 27.6 | |
10 | 1.57 | 19.3 |
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Mendoza-Villa, F.; Manrique-Castillo, E.V.; Passamani, E.C.; Ramos-Guivar, J.A. Towards the Analytical Generalization of the Transcendental Energy Equation, Group Velocity, and Effective Mass in One-Dimensional Periodic Potential Wells with a Computational Application to Common Coupled Potentials. Appl. Sci. 2024, 14, 3987. https://doi.org/10.3390/app14103987
Mendoza-Villa F, Manrique-Castillo EV, Passamani EC, Ramos-Guivar JA. Towards the Analytical Generalization of the Transcendental Energy Equation, Group Velocity, and Effective Mass in One-Dimensional Periodic Potential Wells with a Computational Application to Common Coupled Potentials. Applied Sciences. 2024; 14(10):3987. https://doi.org/10.3390/app14103987
Chicago/Turabian StyleMendoza-Villa, F., Erich V. Manrique-Castillo, Edson C. Passamani, and Juan A. Ramos-Guivar. 2024. "Towards the Analytical Generalization of the Transcendental Energy Equation, Group Velocity, and Effective Mass in One-Dimensional Periodic Potential Wells with a Computational Application to Common Coupled Potentials" Applied Sciences 14, no. 10: 3987. https://doi.org/10.3390/app14103987
APA StyleMendoza-Villa, F., Manrique-Castillo, E. V., Passamani, E. C., & Ramos-Guivar, J. A. (2024). Towards the Analytical Generalization of the Transcendental Energy Equation, Group Velocity, and Effective Mass in One-Dimensional Periodic Potential Wells with a Computational Application to Common Coupled Potentials. Applied Sciences, 14(10), 3987. https://doi.org/10.3390/app14103987