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The second derivative* of the wave function with respect to position (x) is an important component of the Schrodinger equation. If you want an in depth explanation on why that is then I would recommend you go to office hours with Prof. Lavelle or perhaps the TA's because the math behind the schrodinger equation is beyond the scope of what is expected of us. I tried looking up the derivation of the equation and I read only one line of math before getting lost. What's important is that you know the reason that this equation is important: it uses Heisenberg's indeterminancy principle, the wave/particle duality of electrons, and the wave function to construct an equation from which new equations can be derived to represent the shape of electron orbitals on a 3D coordinate system as well as the first three quantum numbers: n, l, and ml.
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