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Illustration Squared magnitude - Normalization condition - Integration over the entire space

Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
Betragsquadrat (Beispiel) - Normierungsbedingung ergibt Wahrscheinlichkeit 1
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For the statistical interpretation of quantum mechanics (Copenhagen interpretation) to make any sense at all, the normalization condition must be fullfilled:\[ \int_{-\infty}^{\infty} |\mathit{\Psi}(x,t)|^2 \, \text{d}x ~=~ 1 \]

The normalization condition states that the probability of finding the particle somewhere in space must be 1. The integral is the area under the \( |\mathit{\Psi}(x,t)|^2 \)-curve.

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