✦ LIBER ✦

Accurate solution to the time-independent Schrödinger equation using Stirling's interpolation formula

✍ Scribed by P.F. Zou

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 403 KB
Volume: 222
Category: Article
ISSN: 0009-2614
DOI: 10.1016/0009-2614(94)00353-x

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✦ Synopsis

Stirling's interpolation formula is used to obtain a matrix representation of the time-independent Schriidinger equation. It is shown that an N-point Stirling interpolation formula is able to give an order of 8'v accuracy to the kinetic energy matrix. The potential matrix is diagonal and can be calculated exactly without involving any integration. Therefore, this formulation is able to yield any desired accuracy for a given discretized real space. A general formula is given explicitly for constructing the Hamiltonian matrix elements to any order of accuracy.