The inner product is supposed to give the probability amplitude for state u turning into state v. Taking a little mini-universe of two dimensions in the complex plane if I rotate vector u by multiplying it by scalar a to get vector v, then I end up that a = u*v/(||u||.||v||); given that the lengths are irrelevant for quantum physics, the numerator is taken as the inner product at a point (with the dot product being its real part). But the inner product is defined as the integral of fg*, not f*g. Why?(adsbygoogle = window.adsbygoogle || []).push({});

Or did I calculate that wrong?

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# Why does the inner produce in Hilbert space use fg* and not f*g?

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