The two-slit and multiple-slit diffraction of electrons have been analyzed by probability amplitude of momentum representation in quantum theory,and the results are in keeping with light's.The quantum eigenstate of the electron diffraction is elaborated.
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments have been explained by some theoretical works. We study electronic double-slit diffraction with a quantum mechanical approach and obtain the following results: (1) When the ratio of ( d + a )/ a = n ( n = 1,2,3,…), orders n ,2 n ,3 n ,… are missing in diffraction pattern. (2) When the ratio of ( d + a )/ a ≠ n ( n = 1,2,3,…), there is not missing order in diffraction pattern. (3) The slit thickness c has a large affect on the electronic diffraction pattern, which is a new quantum effect. We believe that all the predictions in our work can be tested by the electronic double slit diffraction experiment.
We study electronic multiple-slit diffraction with a quantum mechanical approach. Our theoretical results are in good agreement with classical theoretical calculations and we obtain the following resluts: (1) There are N − 2 secondary maxima and N − 1 minima between the two principle maxima in diffraction pattern. (2) As the slit number N increasing, the diffraction intensity increases and the pattern width becomes narrow. (3) The slit thickness c dose not have any influence on diffraction pattern when slit width a is far greater than the electronic wavelength λ, for example, the ratio of a λ = 10, and at the ratio, the missingorder phenomenon can be observed when d+a a = n (n = 1, 2, 3 . . .), where d is the distance of slit-to-slit. (4) When a is not far greater than λ (the ratio of a λ = 500), the slit thickness c has an effect on diffraction pattern. The missing-order phenomenon can be shown only if the slit thickness c is small enough, and it disappears when the slit thickness c becomes large. In addition, the slit thickness c affects the relative diffraction intensity of the diffraction pattern.
It is proved that for a double slit diffraction experiment,superposition principle of probability amplitudes means the probability amplitude of the event that an electron passes through a certain slit and falls on somewhere of the screen has nothing to do with the condition whether or not the other slit is open,from which it is concluded that the probability itself does not obey superposition principle.Consequently,the total probability formula as a relation among the measurable probabilities is invalid herein.As a result,it is unnecessary to give up the classical idea that an electron moves along an orbit,and thereby it is unnecessary to distinguish between classical physics and quantum physics.