### Abstract

Complex energy eigenvalues which specify the location and width of quasibound or resonant states are computed to good approximation by a simple dimensional scaling method. As applied to bound states, the method involves minimizing an effective potential function in appropriately scaled coordinates to obtain exact energies in the D→∞ limit, then computing approximate results for D=3 by a perturbation expansion in 1/D about this limit. For resonant states, the same procedure is used, with the radial coordinate now allowed to be complex. Five examples are treated: the repulsive exponential potential (e^{-r}); a squelched harmonic oscillator (r^{2} ^{e-r}); the inverted Kratzer potential (r^{-1} repulsion plus r^{-2} attraction); the Lennard-Jones potential (r^{-12} repulsion, r^{-6} attraction); and quasibound states for the rotational spectrum of the hydrogen molecule (X ^{1}∑_{g}^{+}, v=0, J=0 to 50). Comparisons with numerical integrations and other methods show that the much simpler dimensional scaling method, carried to second-order (terms in 1/D^{2}), yields good results over an extremely wide range of the ratio of level widths to spacings. Other methods have not yet evaluated the very broad H_{2} rotational resonances reported here (J>39), which lie far above the centrifugal barrier.

Original language | English |
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Pages (from-to) | 3990-3998 |

Number of pages | 9 |

Journal | The Journal of Chemical Physics |

Volume | 98 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Jan 1993 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*98*(5), 3990-3998. https://doi.org/10.1063/1.464027