What would be the motion of electrons in a pi-bond?

[khil_phys]

The title is the question.
Thanks.

 

[Ygggdrasil]

In classical physics, if we want to describe the motion of a particle, we describe its trajectory, the position of the particle at each point in time. Knowing the trajectory of the particle also give us its velocity (and if we know its mass, the momentum) simply by taking the time derivative of the position.

Particles that behave quantum mechanically, such as electrons, obey Heisenberg's uncertainty principle. This principle states that we cannot simultaneously know the position and momentum of a particle. Because knowing the trajectory of a particle tells us the position and momentum of a particle at every point in time, this means that we cannot know the trajectory of any quantum mechanical property (you can even say that these particle cannot have a trajectory). Therefore, you cannot describe the motion of a quantum mechanical particle in the same way that you describe the motion of a classical particle.

The best we can do is to know the wavefunction of the particle — a mathematical construct that describes the probabilities of finding the particle at a given location in space — and how that wavefunction changes over time.

 

[khil_phys]

So, will it's motion will be completely random to us?

 

[Borek]

So, will it's motion will be completely random to us?

You are trying to understand the electron in a molecule in terms of classical physics. It won't work. You will get closer to the reality assuming there is no such thing as a trajectory.