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The bridge between theoretical and experimental physics which utilizes numerical analysis, specifically through the use of software, to solve problems in physics. This tag is NOT intended for use in solving problems on paper. Please note that details of writing and/or debugging code is OFF-TOPIC and should be asked at either Computational Science, Code Review or Stack Overflow.

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Numerical discretization of the Schrodinger equation

i'm solving numerically the Schrodinger time dependent equation, in this case simplified to one dimension, and i don't know at all how to discretize it, or if what i have done its okay. $$i\hbar\frac{ …