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Consider a dynamical system consisting of a single non-relativistic particle of mass $$m$$ moving along the $$x$$-axis in some real potential $$V(x)$$. In quantum mechanics, the instantaneous state of the system is represented by a complex wavefunction $$\psi(x,t)$$. This wavefunction evolves in time according to Schrödinger’s equation: $\label{e3.1} {\rm i}\,\hbar\,\frac{\partial\psi}{\partial t} = -\frac{\hbar^{\,2}}{2\,m}\frac{\partial^{\,2} \psi}{\partial x^{\,2}} + V(x)\,\psi.$ The wavefunction is interpreted as follows: $$|\psi(x,t)|^{\,2}$$ is the probability density of a measurement of the particle’s displacement yielding the value $$x$$. Thus, the probability of a measurement of the displacement giving a result between $$a$$ and $$b$$ (where $$a<b$$) is $\label{e3.2} P_{x\,\in\, a:b}(t) = \int_{a}^{b}|\psi(x,t)|^{\,2}\,dx.$ Note that this quantity is real and positive definite.