Abstract
The quasi-classical approximation is used to determine the positions of the classical turning points upon motion of an electron that is bound by an image field and a constant homogeneous electric field of the same direction. Power expansions of the coordinates of the turning points in a wide range of electron energies and field strengths are obtained. The mechanism of one-dimensional confinement of an electron, which determines a completely discrete spectrum of states, is described. The dependence of the spatial width of the confinement region on the field strength and electron energy is determined. The dependences of the electron energy in different states on the external field strength are calculated numerically. Quasi-classical quantization is performed, and the dependence of the electron energy on the width of the confinement region is determined. The energy interval of a maximum density of electron states is found, which is determined by the dependence of the width of the confinement region on the electric field strength.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Nanoscale Science and Technology, Ed. by R. Kelsall, I. W. Hamley, and M. Geoghegan (Wiley, Chichester, 2005).
P. Harrison, Quantum Wells, Wires and Dots (Wiley, Chichester, 2010).
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Pergamon, New York, 1984; Nauka, Moscow, 2002).
P. M. Echenique and M. E. Uranga, Surf. Sci. 247, 125 (1991).
P. M. Echenique, R. Berndt, E. V. Chulkov, T. Fauster, A. Goldmann, and U. Hofer, Surf. Sci. Rep. 52, 219 (2004).
S. V. Eremeev, S. S. Tsirkin, and E. V. Chulkov, Phys. Solid State 52, 1768 (2010).
P. M. Echenique and M. E. Uranga, Surf. Sci. 247, 125 (1991).
E. V. Chulkov, V. M. Silkin, and P. M. Echenique, Surf. Sci. 391, L1217 (1997).
E. V. Chulkov, V. M. Silkin, and P. M. Echenique, Surf. Sci. 437, 330 (1999).
Th. Fauster, Ch. Reuß, I. L. Shumay, and M. Weinelt, Chem. Phys. 251, 111 (2000); Th. Fauster and M. Weinelt, J. Electron Spectrosc. Relat. Phenom. 114–116, 269 (2001).
P. M. Echenique and J. B. Pendry, Prog. Surf. Sci. 32, 111 (1990).
I. L. Shumay, U. Höfer, Ch. Reuß, U. Thomann, W. Wallauer, and Th. Fauster, Phys. Rev. B 58, 13974 (1998).
W. S. Fann, R. Storz, and J. Bokor, Phys. Rev. B 44, 10980 (1991).
P. M. Echenique, R. Berndt, E. V. Chulkov, Th. Fauster, A. Goldman, and U. Höfer, Surf. Sci. 52, 219 (2004).
E. V. Chulkov, A. G. Borisov, J. P. Gauyacq, D. Sánchet-Portal, V. M. Silkin, V. P. Zhukiv, and P. M. Echenique, Chem. Rev. 106, 4160 (2006).
P. A. Golovinskii and M. A. Preobrazhenskii, Opt. Spectrosc. 118, 191 (2015).
P. A. Golovinskii and M. A. Preobrazhenskii, Tech. Phys. Lett. 41, 720 (2015).
P. A. Golovinskii and M. A. Preobrazhenskii, Opt. Spectrosc. 122, 120 (2017).
R. Langer, Phys. Rev. 15, 669 (1937).
B. M. Karnakov and V. P. Krainov, WKB Approximation in Atomic Physics(Springer, Berlin, 2013).
L. D. Landau and E. M. Lifshits, Quantum Mechanics (Nauka, Moscow, 1974; Pergamon, New York, 1977), rus. p. 339.
A. B. Migdal, Qualitative Methods in Quantum Theory (Nauka, Moscow, 1975) [in Russian].
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), p. 1046.
H. Bateman, Higher Transcendental Functions (McGraw-Hill, New York, 1953).
N. Froman and P. O. Froman, Stark Effect in a Hydrogenic Atom or Ion (Imperial College, London, 2008).
E. S. Manuilovich, V. A. Astapenko, and P. A. Golovinskii, Quantum Electron. 46, 50 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © P.A. Golovinskii, M.A. Preobrazhenskii, 2018, published in Optika i Spektroskopiya, 2018, Vol. 125, No. 3, pp. 395–401.
Rights and permissions
About this article
Cite this article
Golovinskii, P.A., Preobrazhenskii, M.A. Confinement of an Electron in an Image Potential and an External Electrostatic Field. Opt. Spectrosc. 125, 409–415 (2018). https://doi.org/10.1134/S0030400X18090102
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0030400X18090102