Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation Export

@article{citeulike:3872853, abstract = {In this paper, how to overcome the barrier for a finite difference method to obtain the numerical solutions of a one-dimensional Schr\"{o}dinger equation defined on the infinite integration interval accurate than the computer precision is discussed. Five numerical examples of solutions with the error less than 10−50 and 10−30 for the bound and resonant state, respectively, obtained by the Obrechkoff one-step method implemented in the multi precision mode, which include the harmonic oscillator, the P\"{o}schl–Teller potential, the Morse potential and the Woods–Saxon potential, demonstrate that the finite difference method can yield the eigenvalues of a complex potential with an arbitrarily desired precision within a reasonable efficiency.}, author = {Shao, H. and Wang, Z.}, citeulike-article-id = {3872853}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.cpc.2008.08.002}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0010465508002725}, doi = {10.1016/j.cpc.2008.08.002}, issn = {00104655}, journal = {Computer Physics Communications}, keywords = {numerical\_schrodinger}, month = {January}, number = {1}, pages = {1--7}, posted-at = {2009-01-10 08:18:30}, priority = {4}, title = {Arbitrarily precise numerical solutions of the one-dimensional Schr\"{o}dinger equation}, url = {http://dx.doi.org/10.1016/j.cpc.2008.08.002}, volume = {180}, year = {2009} }

TY - JOUR ID - citeulike:3872853 L3 - citeulike-article-id:3872853 N2 - In this paper, how to overcome the barrier for a finite difference method to obtain the numerical solutions of a one-dimensional Schrödinger equation defined on the infinite integration interval accurate than the computer precision is discussed. Five numerical examples of solutions with the error less than 10−50 and 10−30 for the bound and resonant state, respectively, obtained by the Obrechkoff one-step method implemented in the multi precision mode, which include the harmonic oscillator, the Pöschl–Teller potential, the Morse potential and the Woods–Saxon potential, demonstrate that the finite difference method can yield the eigenvalues of a complex potential with an arbitrarily desired precision within a reasonable efficiency. IS - 1 JF - Computer Physics Communications SN - 00104655 EP - 7 TI - Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation VL - 180 SP - 1 KW - numerical_schrodinger AU - Shao, H AU - Wang, Z PY - 2009/01// UR - http://dx.doi.org/10.1016/j.cpc.2008.08.002 ER -