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The kinetic energy partition method applied to quantum eigenvalue problems with many harmonic-oscillator potentials

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Abstract

We generalize the recently developed kinetic energy partition (KEP) method for systems with two competing interactions to solve the quantum eigenvalue problems of a particle interacting with a number of harmonic-oscillator potentials. First, the original formulation of the KEP method is extended to the case with many interaction potentials. Second, we apply the method to the two and three harmonic-oscillators problems, respectively. Finally, the general N harmonic-oscillators system is considered and solved. We show that the KEP method can yield the exact solutions very accurately and efficiently.

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Acknowledgements

This work was partly supported by the MOST of Taiwan, R.O.C. through MOST 104-2221-E-002-032-MY3 and the CQSE of NTU through the CQSE 104 R891401. We thank Dr. Mineo for many useful suggestions.

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Authors and Affiliations

  1. Institute of Applied Mechanics, National Taiwan University, Taipei, 106, Taiwan, ROC

    Yu-Hsin Chen & Sheng D. Chao

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  1. Yu-Hsin Chen
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  2. Sheng D. Chao
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Correspondence to Sheng D. Chao.

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Chen, YH., Chao, S.D. The kinetic energy partition method applied to quantum eigenvalue problems with many harmonic-oscillator potentials. J Math Chem 55, 1322–1341 (2017). https://doi.org/10.1007/s10910-017-0745-9

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  • DOI: https://doi.org/10.1007/s10910-017-0745-9

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