Abstract
In this chapter, we describe the Phase-Amplitude Method (Ph-A) for the representation of the solution of a Schrödinger equation, in which the wave function is described in an efficient way by its amplitude y(r) and the wave phase \(\phi (r)\). Since each of these quantities vary monotonically and slowly with distance, they are much easier to calculate than the wave function itself. An iterative method to solve the non-linear equation for y is described, and the region of convergence of the iterations is examined for two scattering cases: (a) when the potential is smaller than the incident energy (in this case the wave function is oscillatory); and (b) when the potential is larger than the incident energy (this is the case of the classically forbidden region). Various applications and their accuracies are also described in this chapter.
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Rawitscher, G., dos Santos Filho, V., Peixoto, T.C. (2018). The Phase-Amplitude Representation of a Wave Function . In: An Introductory Guide to Computational Methods for the Solution of Physics Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-42703-4_8
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DOI: https://doi.org/10.1007/978-3-319-42703-4_8
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