Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator Lc,α=−d2/dx2+cxα

The completeness of the system of eigenfunctions of the complex Schrodinger operator L c = − d 2 / d x 2 + c x 2 / 3 on the semi-axis in L 2 ( R + ) with Dirichlet boundary conditions is proved for all c: | arg ⁡ c | π / 2 + θ 0 , where π / 10 θ 0 π / 2 is determined as the only solution of a certain transcendental equation.