EIGENVALUE COMPARISONS FOR QUANTUM-SYSTEMS IN A BOX

Comparison theorems are obtained for the first even and odd solutions of Schrodinger's equation -upsilon '' + Q(t)upsilon = lambda upsilon,- l less than or equal to t less than or equal to l with boundary condit ions upsilon(-l) = upsilon(l) = 0. The comparison functions Q(i)(t), i = 1,2, may intersect at a finite number of points within [-l,l]. Imme diate extensions are possible for a more general class of Sturm-Liouvi lle problems, and for problems in unbounded regions. (C) 1998 Publishe d by Elsevier Science B.V.