Physics – Mathematical Physics
Scientific paper
2006-11-02
Physics
Mathematical Physics
21 pages, 10 figures
Scientific paper
We introduce an optimization procedure for the Spectral Method and apply it as an extremely accurate technique for finding the bound states of the time-independent Schrodinger equation. In this method a finite basis is used for approximating the solutions. Although any complete orthonormal basis can be used, we discuss the Fourier basis. We present a detailed comparison between the results obtained by this method and some of the more routine methods. This method is very simple to program, fast, extremely accurate (e.g. a relative error of 10^(-130) is easily obtainable for most problems), very robust and stable. Most importantly, one can obtain the energies and the wave functions of as many of the bound states as desired with a single run of the algorithm.
Gousheh Siamak S.
Mirzaei Mehrnoush
Pedram Pouria
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