Abstract
One of the best known and most widely exploited analogies between classical physics and quantum mechanics is that between the time-independent Schrödinger equation and the Helmholtz equation, i.e., the time-independent form of Maxwell’s equations. Electrons in bulk semiconductors or heterostructures do not behave like waves, and thus cannot be described by the Schrödinger equation unless:
-
(i)
the interactions between electrons and the periodic crystal lattice, and between different electrons, do not appear explicitly in the electron equation of motion
-
(ii)
the collisions between different electrons as well as the interference effects between the wavefunctions of different electrons can be neglected.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baba, T. (1997): IEEE J. Selected Topics Quantum Electron. 3, 808
Birks, T.A., J.C. Knight, and P.S.J. Russell (1997): Opt. Lett. 22, 961
Born, M. and E. Wolf (1970): Principles of Optics, Pergamon Press, London
Campi, D., M. Meliga, and A. Pisoni (1994): IEEE J. Quantum Electron. 30, 2001
Cornelius, C.M. and J.P. Dowling (1999): Phys. Rev. A 59, 4736
Datta, S. (1997): Electronic Transport in Mesoscopic Systems, Cambridge University Press, Cambridge
Datta, S., M.R. Melloch, S. Bandyopadhyay, R. Noren, M. Vaziri, M. Miller, and R. Reifenberger (1985): Phys. Rev. Lett. 55, 2344
de Sterke, C.M., J.N. Bright, P.A. Krug, and T.E. Hammon (1998): Phys. Rev. E 57, 2365
del Alamo, J.A., C.C. Eugster, Q. Hu, M.R. Melloch, and M.J. Rooks (1998): Superlattices and Microstructures 23, 121
Deutsch, I.H., R.J.C. Spreeuw, S.L. Rolston, and W.D. Phillips (1995): Phys. Rev. A 52, 1394
Dowling, J.P., M. Scalora, M.J. Bloemer, and C.M. Bowden (1994): J. Appl. Phys. 75, 1896
Dragoman, D. (2000): J. Appl. Phys. 88, 1
Dragoman, D. and M. Dragoman (1997a): Opt. Commun 133, 129
Dragoman, D. and M. Dragoman (1997b): IEEE J. Quantum Electron. 33, 375
Dragoman, D. and M. Dragoman (1998): Opt. Commun 150, 331
Dragoman, D. and M. Dragoman (1999a): Progr. Quantum Electron. 23, 131
Dragoman, D. and M. Dragoman (1999b): Advanced Optoelectronic Devices, Springer, Berlin, Heidelberg
Egger, S., C.H. Back, J. Krewer, and D. Pescia (1999): Phys. Rev. Lett. 83, 2833
Esaki, L. (1986): IEEE J. Quantum Electron. 22, 1611
Furuya, K. (1987): J. Appl. Phys. 62, 1492
Gaylord, T.K. and M.G. Moharam (1985): Proc. IEEE 73, 894
Gaylord, T.K. and K.F. Brennan (1989): J. Appl. Phys. 65, 814
Gaylord, T.K., E.N. Glytsis, and K.F. Brennan (1989): J. Appl. Phys. 65, 2535
Gaylord, T.K., E.N. Glytsis, and K.F. Brennan (1990): J. Appl. Phys. 67, 2623
Gaylord, T.K., G.N. Henderson, and E.N. Glytsis (1993): J. Opt. Soc. Am. B 10, 333
Henderson, G.N., T.K. Gaylord, and E.N. Glytsis (1991a): Proc. IEEE 79, 1643
Henderson, G.N., E.N. Glytsis, and T.K. Gaylord (1991b): Appl. Phys. Lett. 59, 440
Henderson, G.N., T.K. Gaylord, and E.N. Glytsis (1992): Phys. Rev. B 45, 8404
Heremans, J.J., M.B. Santos, and M. Shayegan (1992): Appl. Phys. Lett. 61, 1652
Heremans, J.J., S. von Molnar, D.D. Awschalom, and A.C. Gossard (1999): Appl. Phys. Lett. 74, 1281
Ji, Y., Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman (2003): Nature 422, 415
Kaji, R. and M. Koshiba (1994): IEEE J. Quantum Electron. 30, 1036
Kavokin, A., G. Malpuech, A. Di Carlo, P. Lugli, and F. Rossi (2000): Phys. Rev. B 61, 4413
Krauss, T.F. and R.M. De La Rue (1996): Appl. Phys. Lett. 68, 1613
Kyriakidis, J. and D. Loss (1998): Phys. Rev. B 58, 5568
Leburton, J.-P. and Yu.B. Lyanda-Geller (1996): Phys. Rev. B 54, 17716
Lenz, G., I. Talanina, and C.M. de Sterke (1999): Phys. Rev. Lett. 83, 963
Lin, S.-W., V.M. Hietala, S.K. Lyo, and A. Zaslaysky (1996): Appl. Phys. Lett. 68, 3233
Liu, R.C., B. Odom, Y. Yamamoto, and S. Tarucha (1998): Nature 391, 263
Monsivais, G., M. del Castillo-Mussot, and F. Claro (1990): Phys. Rev. Lett. 64, 1433
Morandotti, R., U. Peschel, J.S. Aitchinson, H.S. Eisenberg, and Y. Silberberg (1999): Phys. Rev. Lett. 83, 4756
Nakazato, K., R.I. Hornsey, R.J. Blaikie, J.R.A. Cleaver, H. Ahmed, and T.J. Thornton (1992): Appl. Phys. Lett. 60, 1093
Oliver, W.D., J. Kim, R.C. Liu, and Y. Yamamoto (1999): Science 284, 299
Paré, C., L. Gagnon, and P.A. Bélanger (1992): Phys. Rev. A 46, 4150
Park, K.W., S. Lee, M. Shin, J.S. Yuk, E.-H. Lee, and H.C. Kwon (1999): Superlattices and Microstructures 25, 153
Pertsch, T., P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer (1999): Phys. Rev. Lett. 83, 4752
Peschel, U., T. Pertsch, and F. Lederer (1998): Opt. Lett. 23, 1701.
Razavy, M. (1997): Phys. Rev. A 55, 4102
Sakoda, K. (2001): Optical Properties of Photonic Crystals, Springer, Berlin, Heidelberg
Sarangan, A.M. and W.-P. Huang (1994): IEEE J. Quantum Electron. 30, 2803
Scalora, M., M.J. Bloemer, A.S. Pethel, J.P. Dowling, C.M. Bowden, and A.S. Mantra (1998): J. Appl. Phys. 83, 2377
Sivan, U., M. Heiblum, C.P. Umbach, and H. Shtrikman (1990): Phys. Rev. B 41, 7937
Snyder, A.W. and J. Love (1983): Optical Waveguide Theory, Chapman and Hall, London
Sols, F., M. Macucci, U. Ravaioli, and K. Hess (1989): J. Appl. Phys. 66, 3892
Spector, J., H.L. Stormer, K.W. Baldwin, L.N. Pfeiffer, and K.W. West (1990a): Appl. Phys. Lett. 56, 2433
Spector, J., H.L. Stormer, K.W. Baldwin, L.N. Pfeiffer, and K.W. West (1990b): Appl. Phys. Lett. 56, 1290
Spreeuw, R.J.C., J.P. Woerdman, and D. Lenstra (1988): Phys. Rev. Lett. 61, 318
Stanley, R.P., R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch (1994): Appl. Phys. Lett. 65, 2093
Stegeman, G.I. and D.G. Hall (1990): J. Opt. Soc. Am. A 7, 1387
van Houten, H., C.W.J. Beenakker, J.G. Williamson, M.E.I. Broekaart, P.H.M. van Loosdrecht, B.J. van Wees, J.E. Mooij, C.T. Foxon, and J.J. Harris (1989): Phys. Rev. B 39, 8556
Waschke, C., H. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler (1993): Phys. Rev. Lett. 70, 3319
Weisbuch, C. and B. Vinter (1991): Quantum Semiconductor Structures, Academic Press, London
White, S.R. and L.J. Sham (1981): Phys. Rev. Lett. 47, 879
Wilson, D.W., E.N. Glytsis, and T.K. Gaylord (1991): Appl. Phys. Lett. 59, 1855
Winn, J.N., S. Fan, J.D. Joannopoulos, and E.P. Ippen (1999): Phys. Rev. B 59, 1551
Wu, H., D.W.L. Sprung, J. Martorell, and S. Klarsfeld (1991): Phys. Rev. B 44, 6351
Yacoby, A., U. Sivan, C.P. Umbach, and J.M. Hong (1991): Phys. Rev. Lett. 66, 1938
Yeh, P. (1988): Optical Waves in Layered Media, Wiley, New York Zmudzinski, C.A., D. Botez, and L.J. Mawst (1992): Appl. Phys. Lett. 60, 1049
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dragoman, D., Dragoman, M. (2004). Analogies Between Ballistic Electrons and Electromagnetic Waves. In: Quantum-Classical Analogies. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09647-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-09647-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05766-3
Online ISBN: 978-3-662-09647-5
eBook Packages: Springer Book Archive