Accuracy and efficiency of a phase function method solving the first-order nonlinear one-dimensional radial Schrodinger equation
by Smith, Karl Nicholas, Ph.D., POLYTECHNIC INSTITUTE OF NEW YORK UNIVERSITY, 2010, 249 pages; 3443305

Abstract:

Phase shifts are used to calculate the quantum mechanical scattering cross section of a particle by a spherically symmetrical potential. Accurate phase shifts for elastic scattering from a central potential can be calculated via a phase function. Results using this approach are more accurate than methods based on classical “mechanics”.

The problem of finding numerical solutions of the radial Schrödinger equation with a positive energy is a subject of great interest. A phase function method created to find solutions in the asymptotic region where the potential is negligible is studied.

The purpose of this dissertation is to evaluate a variable phase method for obtaining phase shifts. MATHEMATICA 4.1., a high-level programming language is used to construct programs to compare the efficiency and accuracy of the variable phase function method with that of the wave function method. These programs are designed for ease of use for choices of the input parameters and the potential function. Numerical results are based on scattering from the Lennard -Jones (12, 6) potential.
 
AdviserNorman C. Peterson
SchoolPOLYTECHNIC INSTITUTE OF NEW YORK UNIVERSITY
SourceDAI/B 72-04, p. , Mar 2011
Source TypeDissertation
SubjectsAstrophysics; Quantum physics; Atomic physics
Publication Number3443305
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