Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4632085 | Applied Mathematics and Computation | 2010 | 6 Pages |
Abstract
We develop a simple numerical method for solving the one-dimensional time-independent Schrödinger's equation. Our method computes the desired solutions as Taylor series expansions of arbitrarily large orders. Instead of using approximations such as difference quotients for the derivatives needed in the Taylor series expansions, we use recursive formulas obtained using the governing differential equation itself to calculate exact derivatives. Since our approach does not use difference formulas or symbolic manipulation, it requires much less computational effort when compared to the techniques previously reported in the literature. We illustrate the effectiveness of our method by obtaining numerical solutions of the one-dimensional harmonic oscillator, the hydrogen atom, and the one-dimensional double-well anharmonic oscillator.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Asai Asaithambi,