What is meant by ths wave-particle duality of electrons?
Because,In quantum world every particle behave like the wave or other mean they are wave.Or more explicitly explanation:
Particles in the nature,they behave according to the which experiment is done.
When a electron collide another particle,you can imagine that like the billiard ball.But i doble split experiment,particle behave like a wave.They create interferrece pattern or other behaviors of wavenature.
De broglie suggested that,a wavelenght escort the every particle but scale of large and massive body you can not observe it.
As a simple example, consider an electron passing through a very small single slit. It is detected on a distant screen. There are no forces acting on the electron at any time. Classically, we expect the electron to move in a straight line trajectory, and, if we repeat the experiment, all (classical) electrons always hit the screen in the same spot. But that is not what happens! Electrons are not classical particles. Rather, the electron is deflected without benefit of a deflecting force, and when we repeat the experiment, chances are it will be deflected elsewhere and hit the screen in a different location. Repeating the experiment many times gives us the statistical distribution of all possible locations. This angular distribution of scattered electrons looks like the diffraction pattern we would get when we pass light waves through a slit.
But, individual electrons are always detected as particles; we see a dot on the screen. Only when we observe many electrons hitting the screen in different locations at different times do we begin to see wave-like properties emerge . It is the probability distribution of scattered electrons that we identify as wave diffraction. This is what we mean when we say electrons have wave properties. There are many web sites that show the interference pattern emerging one electron at a time.
 A. Tonomura, et al, Amer. J. Phys., 57, 117-120 (1989)
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