### Abstract

The globally uniform semiclassical wave function expresses the solution to the time independent Schrödinger equation in terms of fixed width Gaussian wave packets traveling along a set of trajectories. There is a globally uniform wave function (GUWF) for each value of the Gaussian width parameter γ. Numerical data show that a small Gaussian width is needed in some regions to obtain accurate results, while a broad Gaussian width provides better results in other regions. Since there is a semiclassically valid GUWF for every positive value of γ, it is reasonable to employ the GUWF corresponding to a Gaussian width that provides good results at each value of r. A criterion for the r dependent choice of γ is proposed and tested on one and two dimensional model problems. The results show that the use of an r dependent γ in the GUWF results in improved accuracy for the model problems considered.

Original language | English |
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Article number | 034104 |

Journal | Journal of Chemical Physics |

Volume | 126 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*126*(3), [034104]. https://doi.org/10.1063/1.2424938

**Using an r -dependent Gaussian width in calculations of the globally uniform semiclassical wave function.** / Herman, Michael F.; Sergeev, Alexey.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 126, no. 3, 034104. https://doi.org/10.1063/1.2424938

}

TY - JOUR

T1 - Using an r -dependent Gaussian width in calculations of the globally uniform semiclassical wave function

AU - Herman, Michael F.

AU - Sergeev, Alexey

PY - 2007

Y1 - 2007

N2 - The globally uniform semiclassical wave function expresses the solution to the time independent Schrödinger equation in terms of fixed width Gaussian wave packets traveling along a set of trajectories. There is a globally uniform wave function (GUWF) for each value of the Gaussian width parameter γ. Numerical data show that a small Gaussian width is needed in some regions to obtain accurate results, while a broad Gaussian width provides better results in other regions. Since there is a semiclassically valid GUWF for every positive value of γ, it is reasonable to employ the GUWF corresponding to a Gaussian width that provides good results at each value of r. A criterion for the r dependent choice of γ is proposed and tested on one and two dimensional model problems. The results show that the use of an r dependent γ in the GUWF results in improved accuracy for the model problems considered.

AB - The globally uniform semiclassical wave function expresses the solution to the time independent Schrödinger equation in terms of fixed width Gaussian wave packets traveling along a set of trajectories. There is a globally uniform wave function (GUWF) for each value of the Gaussian width parameter γ. Numerical data show that a small Gaussian width is needed in some regions to obtain accurate results, while a broad Gaussian width provides better results in other regions. Since there is a semiclassically valid GUWF for every positive value of γ, it is reasonable to employ the GUWF corresponding to a Gaussian width that provides good results at each value of r. A criterion for the r dependent choice of γ is proposed and tested on one and two dimensional model problems. The results show that the use of an r dependent γ in the GUWF results in improved accuracy for the model problems considered.

UR - http://www.scopus.com/inward/record.url?scp=33846414292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846414292&partnerID=8YFLogxK

U2 - 10.1063/1.2424938

DO - 10.1063/1.2424938

M3 - Article

VL - 126

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 3

M1 - 034104

ER -