In the past few years several interference and diffraction experiments from light optics have been applied to electron optics:
The diffraction at the half plane, the diffraction at differently formed holes, the diffraction at the wire and the production of electron two-jet interference with the electron-optical Bi-prism, their application for the measurement of the internal potential in the electron interferometer, the implementation of a Mach-Zehnder interferometer for electronen waves and the achievement of two-jet interference by diffraction at two closely neighbouring holes.
Here is of a further, on which electron optics are reported to transferred interference attempt of the light optics: the diffraction of electronen waves at the gap and at periodic arrangements up to five columns, which for the first time also to 3 -, 4 and 5-Strahlinterferenzen in electron optics leads.
The theoretical bases for these attempts are already for a long time created of the light optics and quantum mechanics:
The Schrödinger equation for the freely propagating electron (or the electron beam) reads because U (potential energy) = 0 [math] with [math] of the electron, or because [math] and with [math]. In the light optics a scalar wellentheorie is sufficient in first approximation for the description of the diffraction and interference features instead of the full electromagnetic wellentheorie. A scalar field size S = S(x,y,z,t) is introduced, the "Light moving," which is to meet a wave equation: [math], and whose connection with the observation is given by the demand that the temporal average value of S to the observed intensity be proportional should. If S has a harmonic time dependence (monochromatic light): [math], then the differential equation applies to the complex amplitude [math]: [math].
It agrees with for the psi waves, with which for the psi waves the connection is won to the well-known formulas and results of the light optics here. Since in the light optics the distribution of intensity of the interference features is shown by UUStar, in particular also here the standard PsiPsiStar describes the distribution of intensity with electron interference.
Out the such considerations the following obvious attempt, electron diffraction at the artificially manufactured gap to make for several columns or lattices encounters some technical difficulties, which prevented its implementation so far. These are once the small wavelength of the electron beam, because around reasonable electron optics to float to be able, one must work with intermediate electrons. Here on 50 kV accelerated electrons were always used, whose de Broglie Broglie-Wellenlaenge amounts to about 0.05 A. It is to be provided thus substantially smaller than the atomic dimensions, so that it is in principle impossible, subject with columns, whose width and grating space move in the order of magnitude of the wavelength. This is actually no restriction for such attempts, only one must strive then much for coherent illuminating of the column and the Nachvergroesserung that very fine interference figures. From the wavelength very small in relation to the atomic dimensions a further difficulty follows: there are no transparent substances for electrons, like it it for light gives, an electron beam only in the vacuum is not strewn. Therefore the simplification is not here possible with the production of the column that one prepares it on a transparent carrier, how it is in the light optics e.g. with the diffraction grating cut on glass the case, but one must find a procedure, which permits one to manufacture subject-free column in subject foils whose dimensions are so small that they can be illuminated still intensively enough coherently.