Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. I. Generalities, cubic anharmonicity case

@article{Valle2019RadialAO,
  title={Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. I. Generalities, cubic anharmonicity case},
  author={Juan Carlos del Valle and Alexander V. Turbiner},
  journal={International Journal of Modern Physics A},
  year={2019}
}
For the general [Formula: see text]-dimensional radial anharmonic oscillator with potential [Formula: see text] the perturbation theory (PT) in powers of coupling constant [Formula: see text] (weak coupling regime) and in inverse, fractional powers of [Formula: see text] (strong coupling regime) is developed constructively in [Formula: see text]-space and in [Formula: see text]-space, respectively. The Riccati–Bloch (RB) equation and generalized Bloch (GB) equation are introduced as ones which… 
5 Citations

Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. II. Quartic and sextic anharmonicity cases

In our previous paper I (del Valle–Turbiner, 2019) a formalism was developed to study the general [Formula: see text]-dimensional radial anharmonic oscillator with potential [Formula: see text]. It

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