Numerical approach to the Schrodinger equation in momentum space

Details Numerical approach to the Schrodinger equation in momentum space Numerical approach to the Schrodinger equation in momentum space

2009-10-03

arxiv.org/abs/0910.0574v2

Am. J. Phys. 78, 407 (2010)

Physics

Computational Physics

14 pages, 4 figures, several changes and one figure correction

Scientific paper

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present a numerical approach to the Schrodinger equation in momentum space. After a suitable discretization process, we obtain the Hamiltonian matrix and diagonalize it numerically. By considering a few examples, we show that this approach is ideal for exploring bound-states in a localized potential and complements the traditional (analytical or numerical) treatment of the Schrodinger equation in real-space.

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