Equations 3.6.83.6.8\ref{3.6.11} and 3.6.113.6.11\ref{3.6.14} can be combined to produce ddt∫∞−∞|ψ|2dx=i2m[ψ∗∂ψ∂x−ψ∂ψ∗∂x]∞−∞=0.(3.6.12)(3.6.12)ddt∫−∞∞|ψ|2dx=i2m[ψ∗∂ψ∂x−ψ∂ψ∗∂x]−∞∞=0.\dfrac{d}{dt}\int_{-\infty}^{\infty} \vert\psi\vert^2 dx= \dfrac{\rm{i}}{2m} \left[\psi^*\dfrac{\partial\psi}{\partial x}- \psi\dfrac{\partial\psi^*}{\partial x} \right]_{-\infty}^{\infty} = 0. \label{3.6.15} The above equation is satisfied provided the wavefunction converges lim|x|→∞|ψ|=0(3.6.13)