probability density

 = 0

Increase amplitude

x

The quantum mechanical pendulum

Decrease amplitude

potentialenergy

Note that “amplitude” here means the maximum displacement of the mass of the pendulum, not the complex weight of a term in a quantum superposition. In physics, we often use the same terms to describe different situations, especially when they are related at some abstract level. Can you work out how the general notion of an amplitude is related both to a pendulum and to quantum superpositions?

 = 0.1

 = 0.5

 = 1

 = 2

 = 3

 = 4

 = 5

 = 6