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[5. Heisenberg indeterminacy principle.]
Applications of the indeterminacy principle.
We can use Heisenberg indeterminacy principle to understand why a quantum particle is able to escape from
a potential well. The position q of the particle inside a potential well is strongly localized, thus
the indetermination of its momentum p is high. Since the kinetic energy T of the particle is
a function of its momentum p (T = p²/2m), the indetermination of the energy
is high too. As a consequence of this indetermination, the particle can have enough energy to escape.
Another application of the indeterminacy principle concerns the zeropoint energy. A quantum particle cannot
be completely at rest, because in such case the indetermination of its position and momentum will be zero.
This is true also for a particle at absolute zero. In classical physics, a particle at absolute zero has
no energy at all; in quantum mechanics, a particle at absolute zero is not at rest, so it has a residual
energy.
The indeterminacy principle is applicable also to energy E and time t:
When applied to the electromagnetic field, formula (5.8) states that also in empty space the electromagnetic
field has an energy, called the vacuum energy. Given the equivalence between energy and mass, the vacuum
energy can manifests itself creating couples of shortlived particles and antiparticles, which disappear in
a time interval t determined by equation (5.8).
