### Abstract

In quantum scattering theory, coordinate systems with nontrivial Jacobians may arise and cause difficulty in the reduction of close coupled equations to the desired, simple, obviously Hermitian form { - I(d^{2}/dx ^{2}) + W(x)}f = 0 with W = W^{+}. We consider x to be the translational coordinate, orthogonal to the surface coordinates, and the Schrödinger equation is represented in a basis of surface functions. We introduce a novel wave function factorization which permits reduction to the above form if the basis is (locally) independent of x for arbitrary Jacobian and general weight function for the surface functions. This factorization is compared with the more common factorization where all coordinates are treated equally. Applications to wave function matching and the calculation of surface integrals are mentioned. Several three-dimensional, orthogonal coordinate systems provide examples simplified by the novel factorization.

Original language | English |
---|---|

Pages (from-to) | 1824-1827 |

Number of pages | 4 |

Journal | Journal of Chemical Physics |

Volume | 88 |

Issue number | 3 |

Publication status | Published - 1988 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*88*(3), 1824-1827.

**A novel wave function factorization simplifying the matrix representation of the Schrödinger equation.** / Stechel, Ellen; Webster, Frank; Light, J. C.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 88, no. 3, pp. 1824-1827.

}

TY - JOUR

T1 - A novel wave function factorization simplifying the matrix representation of the Schrödinger equation

AU - Stechel, Ellen

AU - Webster, Frank

AU - Light, J. C.

PY - 1988

Y1 - 1988

N2 - In quantum scattering theory, coordinate systems with nontrivial Jacobians may arise and cause difficulty in the reduction of close coupled equations to the desired, simple, obviously Hermitian form { - I(d2/dx 2) + W(x)}f = 0 with W = W+. We consider x to be the translational coordinate, orthogonal to the surface coordinates, and the Schrödinger equation is represented in a basis of surface functions. We introduce a novel wave function factorization which permits reduction to the above form if the basis is (locally) independent of x for arbitrary Jacobian and general weight function for the surface functions. This factorization is compared with the more common factorization where all coordinates are treated equally. Applications to wave function matching and the calculation of surface integrals are mentioned. Several three-dimensional, orthogonal coordinate systems provide examples simplified by the novel factorization.

AB - In quantum scattering theory, coordinate systems with nontrivial Jacobians may arise and cause difficulty in the reduction of close coupled equations to the desired, simple, obviously Hermitian form { - I(d2/dx 2) + W(x)}f = 0 with W = W+. We consider x to be the translational coordinate, orthogonal to the surface coordinates, and the Schrödinger equation is represented in a basis of surface functions. We introduce a novel wave function factorization which permits reduction to the above form if the basis is (locally) independent of x for arbitrary Jacobian and general weight function for the surface functions. This factorization is compared with the more common factorization where all coordinates are treated equally. Applications to wave function matching and the calculation of surface integrals are mentioned. Several three-dimensional, orthogonal coordinate systems provide examples simplified by the novel factorization.

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M3 - Article

VL - 88

SP - 1824

EP - 1827

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 3

ER -