A quantum-mechanical anharmonic oscillator with a most interesting spectrum

We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter λ. The ground state can be obtained exactly and its energy E0=1 is independent of λ. This solution is valid only for λ>0 because the eigenfunction is not square integrable otherwise. Here we show that the perturbation series for the expectation values are Padé and Borel–Padé summable for λ>0. When λ