Abstract
Comparison theorems are obtained for the first even and odd solutions of Schrödinger's equation − v″ + Q( t) v = λv, − l ≤ t ≤ l with boundary conditions v(− l) = v( l) = 0. The comparison functions Q i ( t), i = 1, 2, may intersect at a finite number of points within [− l, l]. Immediate extensions are possible for a more general class of Sturm-Liouville problems, and for problems in unbounded regions.
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