No title
We discuss spectral properties of the selfadjoint operator−d 2 dt 2 +t k+1 k+1 − α 2 in L 2 (R ) for odd integers k. We prove that the minimum over α of the ground state energy of this operator is attained at a unique point which tends to zero ask tends to infinity. We also show that the minimum is nondegenerate. These questions arise naturally in the spectral analysis of Schr ̈odinger operators w
