A video about the double slit paradox
Fondamental : De Broglie's hypothesis
Let us consider particles of mass , conversely to photons which have no mass.
A photon is both a wave and a corpuscle.
With this idea in mind, De Broglie proposed in 1923 the association of material particles and a wavelength given by :
is the quantity of movement (impulsion) of the particle and is Planck's constant.
Attention : Planck-Einstein equations
Let us consider a material particle of mass , velocity , nonrelativistic quantity of movement and energy .
The relations between wave description and corpuscular description are called Planck-Einstein equations :
By using the pulsation and the wave vector :
We can say that any atomic or subatomic particle is also a wave : it is the famous particle-wave duality of elementary particles in quantum mechanics.
Some order of magnitude : (see rpn.univ-lorraine.fr)
Electrons accelerated with a voltage of , .
Complément : Wave associated to a free particle
The wave associated to the particle, if it moves on the axis can be described as a plane wave :
The phase velocity is :
The group velocity is :
and , so :
The energy of the free particle is equal to its kinetic energy :
Thus, the group velocity (the velocity of a wave pack centered on a pulsation ) is naturally identified to the velocity of a quantum particle.