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For questions regarding the choice and/or appropriateness of conditions necessary to model a particular phenomenon with a partial differential equations.
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Determine numerical infinity for Schrodinger equation $−\psi''(x) + x^ 2 \psi(x) = E\psi(x)$
You should maybe look at the analytical form of these solutions (here's the wikipedia page), this would probably help you to derive a relation between the energy level $n$ and the typical length of yo …