P-stable Exponentially Fitted Methods for the Numerical Integration of the Schrödinger Equation

✍ Scribed by T.E Simos

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 115 KB
• Volume: 148
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1998.6103

✦ Synopsis

A P-stable exponentially fitted method is developed in this paper for the numerical integration of the Schrödinger equation. An application to the bound-states problem (we solve the radial Schrödinger equation in order to find eigenvalues for which the wavefunction and its derivative are continuous and the boundary conditions are satisfied) and the resonance problem (the point of a resonance is that phase changes rapidly through π) of the radial Schrödinger equation indicates that the new method is generally more efficient than the previously developed exponentially fitted methods of the same kind. The method can be applied to any problem of physics and chemistry, which can be expressed as system of coupled second-order differential equations which have oscillatory or periodic solutions. This is because it has the property of the P-stability (i.e., the interval of periodic stability of the proposed method is equal to (0, ∞)) which allow is to integrate successful problems with high oscillatory or periodic solution.