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## Main Question or Discussion Point

How does you normalize a function? Could someone explain it very basically and give an example.

- Thread starter laser123
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How does you normalize a function? Could someone explain it very basically and give an example.

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If a function is not normalized, then we can normalize it by dividing the function by whatever its total integral is. So if we define [itex]A = \int^\infty_{-\infty}f(x)\:dx[/itex], and we define a new function [itex]f'(x) = \frac{f(x)}{A}[/itex], then by definition, [itex]\int^\infty_{-\infty}f'(x)\:dx = 1[/itex], so [itex]f'(x)[/itex] is normalized.

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Thank you! :D

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Also, I should point out that what I gave above was a very generic definition of normalization. In the specific case of quantum mechanics, what we're usually normalizing is the probability density, which is the magnitude squared of the wavefunction. So in practice, the way that you will usually see normalization conditions written is [itex]\int^\infty_{-\infty}|\Psi(x)|^2\:dx = 1[/itex].

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