Automatic computation of quantum-mechanical bound states and wavefunctions
Abstract We discuss the automatic solution of the multichannel Schrodinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Prufer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index. Program summary Program title: MATCAS Catalogue identifier: AEON_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEON_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/license/license.html No. of lines in distributed program, including test data, etc.: 3822 No. of bytes in distributed program, including test data, etc.: 119814 Distribution format: tar.gz Programming language: Matlab. Computer: Personal computer architectures. Operating system: Windows, Linux, Mac (all systems on which Matlab can be installed). RAM: Depends on the problem size. Classification: 4.3. Nature of problem: Computation of eigenvalues and eigenfunctions of multichannel Schrodinger equations appearing in quantum mechanics. Solution method: A CP-based propagation scheme is used to advance the R -matrix in a shooting process. The shooting algorithm is supplemented by a Prufer type mechanism which allows the eigenvalues to be computed according to index: the user specifies an integer k ≥ 0 , and the code computes an approximation to the k th eigenvalue. Eigenfunctions are also available through an auxiliary routine, called after the eigenvalue has been determined. Restrictions: The program can only deal with non-singular problems. Additional comments: Along with the program’s source code, we provide several sample configuration files. Running time: The running time depends on the size n of the problem and the number of eigenvalues/eigenfunctions computed. For a small problem the runtime should not exceed a few seconds.