Heisenberg's indeterminacy equations
Fondamental : Heisenberg's space uncertainty principle
At a given time, the measure of the position and the quantity of movement on the axis both show fundamental indeterminacies.
These are written and .
They verify Heisenberg's indeterminacy equation :
This inequality shows that a quantum state does not give a perfect knowledge of this state in a classical point of view.
The notion of trajectory disappears in quantum mechanics.
A link to the website "Culture sciences physiques" ("Fenêtre ouverte sur la physique quantique") : click HERE
Complément : Heisenberg's indeterminacy principle explains the diffraction of light
Let us consider the diffraction of a light beam by a thin slit of width .
The photon has travelled through a slit.
We can write :
Heisenberg's indeterminacy principle gives :
The indeterminacy on the quantity of movement is given by the vertical coordinate :
Hence the diffraction angle :
The order of magnitude of the angle is the same as the one given by the diffraction theory.
Diffraction can be interpreted thanks to Heisenberg's uncertainty principle.
Exemple : Minimum energy of a particle in an infinite potential well
Let us consider a particle of mass in a "quantum box" : the potential energy of the particle is nil in the well ( ) and infinite elsewhere.
The particle cannot exit the potential well.
The maximum indeterminacy on the position of the particle is approximately :
The indeterminacy principle gives the minimum uncertainty for :
The minimum energy of the particle is then :
Heisenberg's inequalities can determine the minimum energy of containment.
Fondamental : Heisenberg's time indeterminacy principle
Let be the indeterminacy on the measure of an energy and the duration of the measure of this energy. Then :
If the duration of the interaction was nil, then would be infinite and the energy of the particle would not be determined.
Conversely, a fundamental state with an infinite lifetime has a perfectly determined energy.
This inequality asserts that the energy conservation principle cannot be verified. The uncertainty is during a time such as .
With this principle can be explained the concept of virtual particles, messenger of fundamental interactions.
Such a particle of mass (and of energy linked to its mass, ) can exist during a period of time given by the indeterminacy principle :
The previous picture shows a Feynman diagram of the interaction between two electrons : the oblique lines represent the moving electrons and the wavy lines represent the virtual exchanged photon.
A video about the indeterminacy principle