Comment on "Quartic anharmonic oscillator and non-Hermiticity" (1 page)

Alí Mostafazadeh

The analysis of the paper by J.-L. Chen et al. [Phys. Rev. A 67, 012101 (2003)] suffers from a conceptual error. Its results contradict some well-established mathematical facts and are incorrect.

V. C. Kuriakose, K. K. Leelamma, K Babu Joseph

Anirban Pathak, Swapan Mandal

F. T. Hioe, D. B. Macmillen, Elliot W. Montroll

Bijan Kumar Bagchi, A. Banerjee, C. Quesne

Jing‐Ling Chen, L. C. Kwek, C. H. Oh

Using a group-theoretic approach, we investigate some new peculiar features of a general quartic anharmonic oscillator. When the coefficient of the quartic term is positive and the potential is differentiable, we find that continuity of the derivative of the potential forces the nonexistence of an analytic wave function. For the case in which the coefficient of the quartic term is negative, we find that normalizability of the wave function requires non-Hermiticity of the Hamiltonian. Finally, we apply our method to gain some insight on the double well potential.