Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator

Abstract

The power series method has been adapted to compute the spectrum of the Schrodinger equation for central potential of the form $V(r)=\frac{d_{-2}}{r^2}+\frac{d_{-1}}{r}+{\sum }_{i=0}^{\infty }{d}_i{r}^i$. The bound-state energies are given as zeros of a calculable function, if the potential is confined in a spherical box. For an unconfined potential the interval bounding the energy eigenvalues can be determined in a similar way with an arbitrarily chosen precision. The very accurate results for various spherically symmetric anharmonic potentials are presented.

16 pages, 5 figures, published in J. Phys A

References in corpus (2)

• Quantum anharmonic oscillators: a new approach
• Symmetric Triple Well with Non-Equivalent Vacua: Instantonic Approach

Cited by in corpus (4)

• Spherically confined isotropic harmonic oscillator
• Exact and approximate solutions to Schroedinger's equation with decatic potentials
• Quasi-exact solutions for two interacting electrons in two-dimensional anisotropic dots
• Energy Levels of One Dimensional Anharmonic Oscillator via Neural Networks