 A lead ball is hanging from the ceiling on a spring. We then pull it down a bit and let it go. The ball begins to oscillate. The mechanical state of the ball is completely determined by a specification of the position \(x\) and the momentum \(p\) of its center of mass; that is, if we know \(x\) and \(p\), then we know all that there is to know about the mechanical state of the ball. If we now conjoin \(x\) and \(p\) in one vector space we obtain the so-called phase space \(X\) of the system (sometimes also referred to as ‘state  space’).[1]  This is illustrated in Figure 1 for a two-dimensional phase space of the state of a ball moving up and down (i.e., the phase space has one dimension for the ball’s position and one for its momentum).