Reflection and transmission of electrons through surface potential barriers

1964 ◽  
Vol 1 (2) ◽  
pp. 194-212 ◽  
Author(s):  
P.H. Cutler ◽  
J.C. Davis
1985 ◽  
Vol 18 (15) ◽  
pp. 3083-3097 ◽  
Author(s):  
J -M Baribeau ◽  
J Lopez ◽  
J -C Le Bosse

1987 ◽  
Vol 6 (1) ◽  
pp. 55-59 ◽  
Author(s):  
S. Suarez ◽  
A. R. Go�i ◽  
W. Meckbach ◽  
P. R. Focke

2011 ◽  
Vol 60 (4) ◽  
pp. 044210
Author(s):  
Niu Jun ◽  
Zhang Yi-Jun ◽  
Chang Ben-Kang ◽  
Xiong Ya-Juan

10.14311/578 ◽  
2004 ◽  
Vol 44 (3) ◽  
Author(s):  
M. Horák

Potential barriers of different types (rectangular, triangle, parabolic) with a dc-bias and a small ac-signal in the THz-frequency band are investigated in this paper. The height of the potential barrier is modulated by the high frequency signal. If electrons penetrate through the barrier they can emit or absorb usually one or even more energy quanta, thus the electron wave function behind the barrier is a superposition of different harmonics. The time-dependent Schrödinger equation is solved to obtain the reflection and transmission amplitudes and the barrier transmittance corresponding to the harmonics. The electronic current density is calculated according to the Tsu-Esaki formula. If the harmonics of the electron current density are known, the complex admittance and other electrical parameters of the structure can be found.


The reflection and absorption, by the charged spherically symmetric Reissner-Nordström black hole, of an arbitrary superposition of gravitational and electromagnetic waves, with time dependence e iot and analyzed into spherical harmonics of various orders l , are expressed in terms of the complex reflection and transmission amplitudes (for incident waves) by two one-dimensional potential barriers. These amplitudes, expressed in terms of eight quantities (and composing the scattering matrix), are tabulated for various values of o,l (= 2, 3, and 6) and charge of the black hole. By virtue of the coupling of electromagnetic and gravitational perturbations by the charge of the black hole, the energy in an incident wave, which is purely gravitational, is, in part, reflected as electromagnetic waves; and conversely. This transformation of incident gravitational energy into electromagnetic energy (and vice versa) is expressed in terms of a conversion factor C and plotted in a series of graphs as a function of o for various values of l and the charge on the black hole Q * . Finally, the complex frequencies belonging to the quasi-normal modes (i.e., solutions of the underlying wave equations which correspond to purely outgoing waves at infinity and purely ingoing waves at the horizon) are tabulated. It is found that the imaginary part of these frequencies (which determine the damping of arbitrary initial perturbations of the black hole) is very nearly the same for all modes (with different l ’s) and Q * .


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