Wilkinson, Michael
(2001).
*Journal of Physics A: Mathematical and General*, 34(49) pp. 11149–11156.

DOI (Digital Object Identifier) Link: | http://dx.doi.org/10.1088/0305-4470/34/49/328 |
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## Abstract

A new type of basis set for quantum mechanical problems is introduced. These basis states are adapted to describing the dynamics of a Hamiltonian Ĥ which is dependent upon a parameter X. A function f(E) is defined which is an analytic function of E, and which is negligibly small when |E|>>δE, where δE is large compared to the typical level separation. The energy-shell basis set consists of states |ξn(X)} which are derived by applying the operator f(Ĥ(X)-Ē_{n}(X)) to elements of a fixed basis set, where Ē_{n}(X) is an analytic approximation to an eigenvalue E_{n}(X). The energy-shell basis states are combinations of states close to energy E_{n}, but vary more slowly as a function of X than the eigenfunctions | ^{ø}_{n}(X) of Ĥ (X). This feature gives the energy-shell basis states some advantages in analysing solutions of the time-dependent Schrödinger equation.

Item Type: | Journal Article |
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Copyright Holders: | 2001 IOP Publishing Ltd |

ISSN: | 1361-6447 |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 25382 |

Depositing User: | Michael Wilkinson |

Date Deposited: | 08 Apr 2011 09:22 |

Last Modified: | 15 Jan 2016 15:25 |

URI: | http://oro.open.ac.uk/id/eprint/25382 |

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