Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator $L=-d^2/d{x}^2+c{x}^{2/3}$

Abstract

We prove the completeness of the system of eigenfunctions of the complex Schrödinger operator $L=-d^2/d{x}^2+c{x}^{2/3}$ on the semiaxis in $L_2(0,+\infty )$ with Dirichlet boundary conditions for all $c$: $|\arg c|<\pi /2+{\theta }_0$, where ${\theta }_0\in (\pi /10,\pi /9)$ is defined as the only solution of a certain transcendental equation.

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