The Heisenberg uncertainty principle is a way of expressing the qualitative properties of quantum mechanics in an easy to visualize way.
Figure 3.3 is a combination plot of the position
The right of the figure shows what happens if you squeeze down on the
particle to try to restrict it to one position
Heisenberg showed that according to quantum mechanics, the area of the
blob cannot be contracted to a point. When you try to
narrow down the position of a particle, you get into trouble with
momentum. Conversely, if you try to pin down a precise momentum, you
lose all hold on the position.
The area of the blob has a minimum value below which you cannot go.
This minimum area is comparable in size to the so-called
Planck constant, roughly 1
- The Heisenberg uncertainty principle says that there is always a minimum combined uncertainty in position and linear momentum.
- It implies that a particle cannot have a mathematically precise position, because that would require an infinite uncertainty in linear momentum.
- It also implies that a particle cannot have a mathematically precise linear momentum (velocity), since that would imply an infinite uncertainty in position.