I recently stumbled upon the definition of a Relativistic particle:
A relativistic particle is a particle which moves with a relativistic speed; that is, a speed comparable to the speed of light.
However I remember from the university courses that the electrons of an atom are described in term of probability density (cloud).
So my question is that how can we link the concept of trajectory to the one of electron cloud. It seems to me that those concepts are contradictory.
It is the difference between bound states and free particles. A bound state is a solution of a quantum mechanical equation, the wave function $Ψ$ a complex function and $Ψ^*Ψ$ is the probability of finding the electron about the nucleus at a specific (x,y,z,t). The electrons are in orbitals, not orbits, which is the naive "cloud" description. See Quantum microscope’ peers into the hydrogen atom.
What lies within the H atom? Experimental observation of the transverse nodal structure of four atomic hydrogen Stark states. The images in the middle show experimental measurements.
And here is an electron, free, leaving an interaction vertex:
The curly line was produced by an electron that was struck by one of twelve $K^-$ passing beam particles in a liquid hydrogen bubble chamber. It curves in an applied magnetic field and loses energy rapidly, spiralling inwards.
Its energy and momentum can be solved with the classical equation of a charged particle in a magnetic field losing energy due to the medium it interacts with. So it is a trajectory in the classical sense.The tracks of the beam particles are also a trajectory in the classical sense.
So, my question is how can we link the concept of trajectory to one of the electron clouds.
The answer is, You can't do so, and You shouldn't since the trajectory is a classical concept while electrons are quantum objects and don't possess any trajectory.
There are, of course, relativistic quantum objects. The theory for dealing with these is called Quantum field theory.
Naively you can consider an electron plane wave that has a fixed momentum (and hence velocity), If this velocity is relativistic then you are in the relativistic regime and the particle said to be relativistic particle.
So my question is that how can we link the concept of trajectory to the one of electron cloud.
This is easy if you model a partially-localized electron with a wave packet. The group velocity of this wave packet will be the classical velocity of the particle. Absolute square of corresponding wavefunction will be particle's probability density.
An example of this wave-packet approach applied to an atom is given here.
