𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Orbital HP-Clouds for solving Schrödinger equation in quantum mechanics

✍ Scribed by J.S. Chen; W. Hu; M. Puso

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
439 KB
Volume
196
Category
Article
ISSN
0045-7825

No coin nor oath required. For personal study only.

✦ Synopsis

Solving Schro ¨dinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions, in addition to the highly coupled nature between wave functions. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schro ¨dinger equation under the framework of HP-Clouds. An intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed. Due to the employment of higher order basis functions, a higher order stabilized conforming nodal integration is developed. The proposed methods are implemented using the density functional theory for solution of Schro ¨dinger equation. Analysis of several single and multi-electron/nucleus structures demonstrates the effectiveness of the proposed method.

📜 SIMILAR VOLUMES

Sinc collocation in quantum chemistry: S
Sinc collocation in quantum chemistry: Solving the planar coulomb Schrödinger equation
✍ Vasilios G. Koures; Frank E. Harris 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 515 KB

Dirac bra-ket notation is introduced for the Whittaker cardinal (Sinc) functions and a previously unreported completeness relation for these quantities is presented and derived. With the use of this completeness relation it becomes simple to transform to a Sinc-basis the eigenvalue equations arising

A Fourier-Bessel expansion for solving r
A Fourier-Bessel expansion for solving radial Schrödinger equation in two dimensions
✍ H. Taşeli; A. Zafer 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 161 KB 👁 1 views

The spectrum of the two-dimensional Schrodinger equation for polynomial oscillators bounded by infinitely high potentials, where the eigenvalue problem is defined on a w . finite interval r g 0, L , is variationally studied. The wave function is expanded into a Fourier᎐Bessel series, and matrix elem