= Sturm oscillation theorem
{c}
For a real one-dimensional <Sturm-Liouville problem> with separated self-adjoint boundary conditions and discrete simple spectrum, the eigenfunction for the $n$th eigenvalue has exactly $n$ interior zeros, numbering from zero. For a confining real <Schrödinger operator> on the line, the same ordering makes the ground state nodeless and the first excited state have one node. If the potential is even, uniqueness and reflection symmetry imply that these states are respectively even and odd.
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