Macroscopically
a wave is an extensive disturbance in a medium (for example water serves as the medium for the ripples on its surface).
When several waves come together they combine constructively or destructively, i.e. they interfere.
When such a wave passes through a small aperture it is diffracted and
spreads out into the shadow zone.
In quantum mechanics the probability distribution of a particle is obtained from a wave function.
This wave can diffract and interfere just like a classical wave.
The effect of diffraction on the probability distribution of a quantum particle can be studied by considering a wave packet that passes through a narrow slit. In the following animations the initial wave packet is taken to be
with and
.
The animations show that