Journal article
Arbitrarily accurate eigenvalues for one-dimensional polynomial potentials
Journal of physics. A, Mathematical and general, Vol.35(41), pp.8831-8846
10/18/2002
DOI: 10.1088/0305-4470/35/41/314
Abstract
We show that the Riccati form of the one-dimensional Schrödinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When G and the potential (as for anharmonic oscillators) are polynomials the solutions of these two equations are entire functions (L and K) and the zeros of K are identical to those of the wavefunction. Requiring such a zero at a large but finite value of the argument yields low energy eigenstates with exponentially small errors. Approximate formulae for these errors are provided. We explain how to choose G in order to dramatically improve the numerical treatment. The method yields many significant digits with modest computer means. We discuss the extension of this method in the case of several variables.
Details
- Title: Subtitle
- Arbitrarily accurate eigenvalues for one-dimensional polynomial potentials
- Creators
- Y Meurice
- Resource Type
- Journal article
- Publication Details
- Journal of physics. A, Mathematical and general, Vol.35(41), pp.8831-8846
- DOI
- 10.1088/0305-4470/35/41/314
- ISSN
- 0305-4470
- eISSN
- 1361-6447
- Language
- English
- Date published
- 10/18/2002
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984199707402771
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