# Tag Info

## Hot answers tagged notation

1

I'm taking a QM course and I'm trying to make sense of why observables are sometimes conjugated for no apparent reason in their inner products. There is a lot of confusion even already. Let's start with the basics. There are vectors and operators and an inner product. If everything was finite dimensional the vectors would be complex column vectors, the ...

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It might help if we use a little mathematics to clear up what's happening here; I assume that you are familiar with vector spaces equipped with an inner product. These when first introduced are over the reals, and are finite-dimensional. In the standard presentation of QM, these two things changes: we no longer work over the real numbers, but the complex ...

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Let $V$ be an (in)-finite dimensional vector space, $V^*$ its dual and let $$\sigma\colon V\times V\to \mathbb{C}$$ be a scalar product, that is $\sigma(v,u)\in\mathbb{C}$ on any pair of vectors in $V$. At this point notice the following: Proposition: every bilinear form $\sigma$ on $V$ induces a map $\rho\colon V\to V^*$ as \$\rho_v(\cdot) = ...

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