information:classification, structural:summarization, information:extraction
Implication

Now let x 0 {\displaystyle x_{0}} be some random point (where both wave functions are defined) and set: c 1 = ψ 2 (x 0, 0) a {\displaystyle c_{1}={\frac {\psi _{2}(x_{0},0)}{a}}} and c 2 = − ψ 1 (x 0, 0) a {\displaystyle c_{2}={\frac {-\psi _{1}(x_{0},0)}{a}}} with a = | ψ 1 (x 0, 0) | 2 + | ψ 2 (x 0, 0) | 2 > 0 {\displaystyle a={\sqrt {|\psi _{1}(x_{0},0)|^{2}+|\psi _{2}(x_{0},0)|^{2}}}>0} (according to the premise no nodes).