# Technical question about Nikolic' Quantum Myths

I am referring to the http://arxiv.org/abs/quant-ph/0609163" [Broken] discussed at length in other threads with a purely technical question to help me understand more of the paper.

On page 12, formula 26 defines the norm of a vector as

$$\langle\psi|\psi\rangle = \psi_1^*\psi_1 + \psi_2^*\psi_2 .$$

My question is: isn't there a square root missing to get a norm. When I look up my lecture notes on functional analysis, a norm on a Hilbert space is defined by

$$||f|| = \sqrt{(f,f)}$$

where $(\cdot,\cdot)$ is the scalar product. If the above formula 26 would nevertheless be correct, I would end up with a scalar product with a square in, which is not linear and therefore not a scalar product.

What am I confusing here?

Thanks,
Harald.

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Square root is indeed missing. Or he meant to write norm squared.

Demystifier
Gold Member
Or he meant to write norm squared.
Yes he did. Even the the mass squared is sometimes called mass by physicists, especially relativists. technical question about Nikolic' Quantum Myths (2nd round)

Thanks for the answers so far. Reading on in http://arxiv.org/abs/quant-ph/0609163" [Broken], I next stumble over formula 28. There I get

$$p_1=|\langle \phi_1|\psi\rangle|^2 = |\sqrt{1^*\psi_1 + 0\psi_2}|^2 = |\sqrt{\psi_1}|^2 = |\psi_1| = \sqrt{\psi_1^*\psi_1} .$$

This, however, contradicts the equation in the paragraph before formula 24, where it reads $p_1 = \psi_1^*\psi_1$.

My question is, whether formula 28 should rather start with $\sqrt{p_1}$ or whether actually it should read $p_1 = \sqrt{\psi_1^*\psi1}$ in the paragraph before 24?

Thanks,
Harald

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Demystifier
Gold Member
$$|\langle \phi_1|\psi\rangle|^2 = |\sqrt{1^*\psi_1 + 0\psi_2}|^2$$
This is wrong. The correct statement is
$$|\langle \phi_1|\psi\rangle|^2 = |1^*\psi_1 + 0\psi_2|^2$$
To repeat, <a|a> denotes the norm SQUARED.

This is wrong. The correct statement is
$$|\langle \phi_1|\psi\rangle|^2 = |1^*\psi_1 + 0\psi_2|^2$$
To repeat, <a|a> denotes the norm SQUARED.
Arrrgh, this missing square of the norm got me all messed up. I should have read my own initial post .

Thanks for getting me back on the right track.
Harald.