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Spectrum guided integration for nonrelativistic quantum-mechanical problems


Gläßle,  Thomas
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society,;

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Gläßle, T. (2012). Spectrum guided integration for nonrelativistic quantum-mechanical problems. Bachelor Thesis, Ruprecht-Karls-Universität, Heidelberg, Germany.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-42E3-5
The numerical integration of the Schrödinger equation is an enduring challenge for modern computer algorithms. Today, many numerical schemes with different numerical properties are available for its solution. A complementary approach is to alter the physical description of the problem to improve the numeric performance of the used integration algorithm. The spectrum-guided-integration utilizes a gauge transformation to render the wave function easier to master for numerical algorithms. This method has proven to be of particular value if the quantum system behaves much like its classical analogon. In this thesis the technique is generalized for usage on systems that may feature strong quantum effects. An estimate of the error improvement is discussed. To illustrate and check the considerations, the methods are applied in three model systems. These are the harmonic oscillator, a laser interaction with a bound state in a softcore potential and a scattering event with a central softcore potential.