Calculation of Upper and Lower Bounds to Oscillator Strengths

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Abstract
A procedure is described for calculating rigorous upper and lower bounds to dipole oscillator strengths and is illustrated numerically with various simple applications to the hydrogen molecular ion. The procedure appears to give a good account of the actual errors which may arise in the conventional method based on energy minimization of the two states. In addition, specific regions of configuration space which are important for the oscillator strength, but perhaps not for the energy, are singled out and emphasized automatically.