Research ArticleOpen AccessGoogle Scholar indexed
Charged Particle in a Flat Box with Static Electromagnetic Field and Landau’s Levels
Departamento de Física, Universidad de Guadalajara, Guadalajara, México
Departamento de Física, Universidad de Guadalajara, Guadalajara, México
- 1 Departamento de Física, Universidad de Guadalajara, Guadalajara, México
- 2 Departamento de Física, Universidad de Guadalajara, Guadalajara, México
Journal of Modern Physics·Volume 11 (2020)·Pages 1731–1742·Published 12 October 2020·DOI10.4236/jmp.2020.1110106
Copy link · social · email
Abstract
We study the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field. Contrary to Landau’s solution with constant magnetic field transverse to the box and using Fourier transformation, we found a full solution for the wave function which is different from that one given by Landau, and this fact remains when static electric field is added. However, the Landau’s levels appear in all cases.
KeywordsLandau’s LevelsQuantum Hall EffectFlat Box
- Klitzing, K.V., Dorda, G. and Pepper, M. (1980) Physical Review Letters, 45, 494. https://doi.org/10.1103/PhysRevLett.45.494
- Landau, L.D. and Lifshitz, E.M. (2013) Quantum Mechanics: Non-Relativistic Theory, Volume 3. Elsevier, Amsterdam.
- Ando, T., Matsumoto, Y. and Uemura, Y. (1975) Journal of the Physical Society of Japan, 39, 279-288. https://doi.org/10.1143/JPSJ.39.279
- Laughlin, R.B. (1981) Physical Review B, 23, 5632. https://doi.org/10.1103/PhysRevB.23.5632
- Halperin, B.I. (1982) Physical Review B, 25, 2185. https://doi.org/10.1103/PhysRevB.25.2185
- Laughlin, R.B. (2000) Uspekhi Fizicheskikh Nauk, 170, 292-303. https://doi.org/10.3367/UFNr.0170.200003f.0292
- Tsui, D.C., Stormer, H.L. and Gossard, A.C. (1982) Physical Review Letters, 48, 1559. https://doi.org/10.1103/PhysRevLett.48.1559
- Laughlin, R.B. (1983) Physical Review Letters, 50, 1395-1398. https://doi.org/10.1103/PhysRevLett.50.1395
- Jain, J.K. (1989) Physical Review Letters, 63, 199-202. https://doi.org/10.1103/PhysRevLett.63.199
- Bernevig, B.A., Hughes, T.L. and Zhang, S.-C. (2006) Science, 314, 1757-1761. https://doi.org/10.1126/science.1133734
- König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L.W., Qi, X.-L. and Zhang, S.-C. (2007) Science, 318, 766-770. https://doi.org/10.1126/science.1148047
- Li, J., Chu, R.-L., Jain, J.K. and Shen, S.-Q. (2009) Physical Review Letters, 102, Article ID: 136806. https://doi.org/10.1103/PhysRevLett.102.136806
- Jiang, H., Wang, L., Sun, Q.-F. and Xie, X.C. (2009) Physical Review B, 80, Article ID: 165316. https://doi.org/10.1103/PhysRevB.80.165316
- Groth, C.W., Wimmer, M., Akhmerov, A.R., Tworzydlo, J. and Beenakker, C.W.J. (2009) Physical Review Letters, 103, Article ID: 196805. https://doi.org/10.1103/PhysRevLett.103.196805
- Mong, R.S.K., Essin, A.M. and Moore, J.E. (2010) Physical Review B, 81, Article ID: 245209. https://doi.org/10.1103/PhysRevB.81.245209
- Pesin, D. and Balents, L. (2010) Nature Physics, 6, 376-381. https://doi.org/10.1038/nphys1606
- Fu, L. and Kane, C.L. (2008) Physical Review Letters, 100, Article ID: 096407. https://doi.org/10.1103/PhysRevLett.100.096407