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

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

2005-12-12

arxiv.org/abs/quant-ph/0512087v1

J. Phys. A: Math. Gen. 38 7743-7755 (2005)

Physics

Quantum Physics

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

Scientific paper

10.1088/0305-4470/38/35/008

The power series method has been adapted to compute the spectrum of the Schrodinger equation for central potential of the form $V(r)={d_{-2}\over r^2}+{d_{-1}\over r}+\sum_{i=0}^{\infty} d_{i}r^i$. 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.

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