We present an alternative approach to separable problems in quantum mechanics and apply it to the time-independent Schrodinger equation for the hydrogen molecular ion under the Born-Oppenheimer approximation. The roots of a pair of Hankel determinants, built from the Taylor coefficients of the regularized logarithmic derivative of the eigenfunctions resulting from separation in spheroidal coordinates, yield the separation constant and the internuclear distance accurately for every value of the electronic energy. The method converges rapidly, giving tight upper and lower bounds to the basic parameters.