Can someone explain the diffraction of electrons through a single hole?

[Goodver]

Could anyone please explain the mechanism of diffraction of electrons through the single hole. Have a look on the picture attached.

It says if we would shoot only one electron at a time, the pattern would be the same.

Things which are confusing me:

1. If the source of emitted electrons is far from the grating (holes), then the direction of "flying" electrons is perpendicular to the plane of holes. According to De Broglie particles propagate as waves and not as a straight line. Since electrons are not accelerating, they are not emitting any waves by themselves. Thus the electron can be seen as a flying sphere (combined waves in all planes) right?.

Why the electron is changing its direction when passing through the whole? What influence on changing of its direction?

I understand how diffraction works in uniform medium (Huygens–Fresnel principle), but... see 2

2. According to Huygens–Fresnel principle, every point to which a luminous disturbance reaches becomes a source of a spherical wave.

Since the experiment on the picture happens in vacuum, then what is a "point to which a luminous disturbance reaches" in vacuum? Like I understand if its in water or any other uniform medium, but what can be hit in vacuum?

 

[Goodver]

Attachment is from "University physics with modern physics, Yound and Freedman, 13 edition"

 

[mathman]

You have stumbled upon the basic problem with quantum theory. It works, but it is almost impossible to explain, particularly if you are looking for a classical analogy.

Electrons have wave properties, so they diffract somehow.

 

[Bill_K]

I understand how diffraction works in uniform medium (Huygens–Fresnel principle)

Then you should have no trouble with electron diffraction. It is conceptually the same.

Could anyone please explain the mechanism of diffraction of electrons through the single hole.

There is no mechanism. The reason it happens is that the probability amplitude for the electron obeys the Schrödinger Equation, and the boundary conditions for it are altered by the presence of the slit, and this changes the solution.

1. If the source of emitted electrons is far from the grating (holes), then the direction of "flying" electrons is perpendicular to the plane of holes. According to De Broglie particles propagate as waves and not as a straight line. Since electrons are not accelerating, they are not emitting any waves by themselves. Thus the electron can be seen as a flying sphere (combined waves in all planes) right?.

No, an electron is not to be thought of as a little sphere, in any sense. A beam of electrons traveling in a single direction is represented as a plane wave.

Why the electron is changing its direction when passing through the whole? What influence on changing of its direction?

It interacts with the walls of the slit, and momentum is transferred from slit to particle.

2. According to Huygens–Fresnel principle, every point to which a luminous disturbance reaches becomes a source of a spherical wave. Since the experiment on the picture happens in vacuum, then what is a "point to which a luminous disturbance reaches" in vacuum? Like I understand if its in water or any other uniform medium, but what can be hit in vacuum?

Huyghens principle does not require something to be hit. It's a heuristic way to visualize a solution of the wave equation. The wave propagates itself continuously, as if all points on the wavefront were acting as little transmitters, but that does not mean there's a bunch of tiny little physical objects present to do the transmitting.

 

[Goodver]

Bill_K, that was really helpful, had to reread some facts I thought were clear for me.

If you don't mind, could you please also correct my logic expressed in the following questions as well?

1. Huygens–Fresnel principle applies for all waves, right?
Mechanical when we are dealing with mass and momentums (water for instance)
and
Electromagnetic/quantum when we deal with photons (no mass)

2. There is no explanation why a wave propagates such a way yet? Like why each next point of a wave is a source of lateral wave which propagates in all directions (sphere).

3. Before I thought that electron travels as depicted in pic. a. Is my logic presented on the attached picture correct now?