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New numerical methods applied to solving the one-dimensional eigenvalue problem
Abstract
Two new numerical methods, the log derivative and the renormalized Numerov, are developed and applied to the calculation of bound-state solutions of the one-dimensional Schroedinger equation. They are efficient and stable; no convergence difficulties are encountered with double minimum potentials. A useful interpolation formula for calculating eigenfunctions at nongrid points is also derived. Results of example calculations are presented and discussed.
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Cited by
Reversing hydride-ion formation in quantum-information experiments with Be +
Sawyer, B. C., Bohnet, J. G., Britton, J. W., & Bollinger, J. J. (2015) · Physical Review A · doi:10.1103/physreva.91.011401 · Cited by 27
Metadata
- Authors
- Johnson, B. R.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1977-11-01
- Volume
- 67
- Issue
- 9
- Pages
- 4086-4093
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2029270491
- Cited by
- 617
- References
- 0
- FWCI
- 6.36
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: New numerical methods applied to solving the one-dimensional eigenvalue problem. https://app.cochat.ai/papers/10.1063/1.435384
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- Johnson, B. R. (1977). New numerical methods applied to solving the one-dimensional eigenvalue problem. The Journal of Chemical Physics. https://doi.org/10.1063/1.435384
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
