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Quartic anharmonic oscillator and non-Hermiticity
Citation
Chen, J.-L., Kwek, L. C., & Oh, C. H. (2003). Quartic anharmonic oscillator and non-Hermiticity. Physical Review A, 67(1), Article 012101. https://doi.org/10.1103/PhysRevA.67.012101
Abstract
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.
Date Issued
2003
Publisher
American Physical Society
Journal
Physical Review A