Wavepacket:
from one wave one can almost obtain a particle

The wavepacket and its Fourier components
a) This wavepacket is obtained by great amount of boundless sinus-like waves layering. And this is shown below
b) Few Fourier components of wavepacket

The opportunity to obtain particle from wave is to construct the wavepacket. The wavepacket is the wave limited in the space region length l as is shown on the Figure. Since the squared amplitude in given point is proportional to the probability to detect the particle in this point, there is a high probability to detect the particle somewhere inside this area which is determined by the wave packet and contrary to it, the probability to detect the particle outside this area is about 0. Therefore the possible value for x-coordinate of the particle spreads over the cramped region with the length l:

Δx = l

It can be look like if we could take for the wavelength of the wavepacket the length , which is shown on the illustration and that we associate the wavepacket impulse with the following exact meaning:

pm = h/λm

However, the strict mathematical formulation of quantum mechanics let us to apply this relationship only on boundless sinus-like waves. But fortunately wavepacket of finite length can be represented by boundless sinus-like waves series of different wavelengths which look like the shown on the figure waves. These sinus-like waves with different wavelengths are also referred to as Fourier components of wavepacket (Joseph Fourier). When the wavelengths (or frequencies), amplitudes and phases of these waves are chosen in so way that they coincide with each other in time, one will have finally the wave illustrated on the upper figure.

Almost all Fourier components have the wavelengths that lay between λ1 and λ2, having the following meanings

1/λ1 = 1/λm + 1/2l oder 1/λ2 = 1/λm− 1/2l

The meaning of λm lays between λ1 and λ2. The corresponding impulses are the following:

p1 = h/λ1 = h/λm + h/2l = pm + h/2l

and

p2 = h/λ2 = h/λm− h/2l = pm − h/2l

That's why the impulse corresponding to the wavepacket isn't precisely defined quantity, but rather are spread in the following region:

Δpx ≈ p1 − p2

or
Δpx ≈ h/l

From this formula and Δx = l one can obtain

Δpx Δx ≈ h

The Heisenberg uncertainty principle is the inner conception of such wavepackets.

In the case of electron (or any other particle with the nonzero rest mass) each Fourier component is the de Broglie wave. The de Broglie wave speed is as follows

V = c²/v

The expression for particle impulse, p = h/λ, and p = mv, consists in the definite meaning of Fourier component wavelength λ to which definite particle speed meaning V corresponds. Therefore the speed V of different Fourier components differs for different wavelengths. This is the dispersion phenomenon that is similar to the light passing through glass. Due to the great amount of Fourier components in one wavepacket, the subsequent Fourier components disperse more and more. Though one obtains the above-shown wavepacket, its not the static wave in time.
The next process (dependence on time) is shown on the following illustration.

The divergence of de Broglie wavepacket when spreading in the space.

If the wavepacket moves forward, it begins to spread by itself. The speed of left border point L is slower than the speed of right border point R. These is caused by the uncertainty principle (because the particle speed isn't exactly defined quantity). The envelope line of wavepackets will be clearly understood when one looks on the illustration where it's marked as the border between the light wavepackets and dark background. And P is the envelope line maximum point. The speed of point P is also referred to as the group speed of the wavepacket

vm = pm/m = h/mλm

The speed of P is the average speed of a particle, which is reasonable result.

Now we can solve the contradiction that de Bloglie wave speed is c²/v , that is not equal to v and even more than c. Look at the wave inside the envelope line and the wave crest p which is marked by bold point on the illustration. This wave crest p moves faster than the envelope line maximum P

Vm = c²/vm

This is the Fourier component speed having the average wavelength λm. And it is also referred to as the wavepacket phase speed. That's why the wave crest p moves faster than the envelope line from left end L towards right end R of the wavepacket. The waves always come from L and disappear at R.

We should not be afraid of anything whether the phase speed Vm is greater than light speed c. The electron that is physically important structure stays inside of the envelope line (which has the group speed vm) slowly moving forward and thus it can never reach the speed greater than the speed of light.
One can find some Java-Applets which describe the movement of wavepacket here.