Physics – Computational Physics
Scientific paper
2006-09-21
J.Comput.Phys.227:2970-2976,2008
Physics
Computational Physics
10 pages, 1 figure. Submitted to Phys. Rev. Lett
Scientific paper
10.1016/j.jcp.2007.11.028
A new numerical treatment in the Crank-Nicholson method with the imaginary time evolution operator is presented in order to solve the Schr\"{o}dinger equation. The original time evolution technique is extended to a new operator that provides a systematic way to calculate not only eigenvalues of ground state but also of excited states. This new method systematically produces eigenvalues with accuracies of eleven digits with the Cornell potential that covers non-perturbative regime. An absolute error estimation technique based on a power counting rule is implemented. This method is examined with exactly solvable problems and produces the numerical accuracy down to 10$^{-11}$.
Kang Daekyoung
Won Eunil
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