# 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

- PhysicsInternational Journal of Modern Physics A
- 2020

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…

### Anharmonic oscillator: a solution

- Physics, MathematicsJournal of Physics A: Mathematical and Theoretical
- 2021

It is shown that for the one-dimensional quantum anharmonic oscillator with potential V(x) = x 2 + g 2 x 4 the perturbation theory (PT) in powers of g 2 (weak coupling regime) and the semiclassical…

### Two-body neutral Coulomb system in a magnetic field at rest: From hydrogen atom to positronium

- PhysicsPhysical Review A
- 2020

A simple uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant…

### Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of 56 Ni and 116 Sn

- Physics
- 2020

The analytical solutions of the radial D-dimensional Schrödinger equation for the Yukawa potential plus spin-orbit and Coulomb interaction terms are presented within the framework of the…

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