𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The collocation method based on a generalized inverse multiquadric basis for bound-state problems

✍ Scribed by Xu-Guang Hu; Tak-San Ho; Herschel Rabitz

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
764 KB
Volume
113
Category
Article
ISSN
0010-4655

No coin nor oath required. For personal study only.

✦ Synopsis

The generalized inverse muldquadric basis function ( ! +c21[xll 2 )-8/2, where c > 0, fl > d, and x E ]~d, is introduced for numerically solving the bound-state Schr6dinger equation. Combined with the collocation method, this basis function can yield accurate eigenvalues of highly excited vibrations, as demonstrated by using one-and two-dimensional potentials. In addition, the generalized inverse multiquadric basis function is as flexible and simple as the Gaussian basis. The multiquadric form does not call for semiclassically distributed grid points and specially scaled exponential parameters as required in the latter case 1o achieve high accuracy.

📜 SIMILAR VOLUMES

A filter diagonalization for generalized
A filter diagonalization for generalized eigenvalue problems based on the Sakurai–Sugiura projection method
✍ Tsutomu Ikegami; Tetsuya Sakurai; Umpei Nagashima 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 756 KB

The Sakurai-Sugiura projection method, which solves generalized eigenvalue problems to find certain eigenvalues in a given domain, was reformulated by using the resolvent theory. A new interpretation based on filter diagonalization was given, and the corresponding filter function was derived explici

A Padé Extrapolated Inverse Power Method
A Padé Extrapolated Inverse Power Method for Coupled Schrödinger-like Equations Applied to the Two-Body Relativistic Bound State Problem in Quantum Electrodynamics
✍ H.W. Crater 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 651 KB

We adapt the inverse power method to the solution of the eigenvalue problem associated with recently developed forms of coupled two-body Dirac equations. A Pauli reduction of these equations leads to coupled Schrödinger-like equations which we solve using central difference methods. Our adaptation t

On an Riesz basis of generalized eigenve
On an Riesz basis of generalized eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid
✍ Aref Jeribi; Abdelkader Intissar 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 230 KB

In this paper we prove that the system of generalized eigenvectors of the operator (I + εK) -1 × d 4 /dx 4 forms a Riesz basis of L 2 (]-L, L[) where K is the integral operator with kernel the Hankel function of the first kind and order 0. This operator was introduced in J.