On the Spectrum of the Local P 2 Mirror Curve.

We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi-Yau threefold called local P 2 in the case of complex values of Planck's constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.