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Results tagged with hilbert-space
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user 370215
This tag is for questions relating to Hilbert Space, a vector space equipped with an inner product, an operation that allows defining lengths and angles, and the space is complete. It arises naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces having the property that it is complete. Applies also to pre-Hilbert spaces, rigged Hilbert spaces, and spaces with negative norm or zero-norm states.
1
vote
Position Eigenstate and Parity Operator
The main confusion is that $\vert x \rangle \neq \vert -x \rangle$. The Dirac "kets" are just a shorthand for evaluating a wave function at some position. The action of a linear form $\langle \psi \ve …
- 482
4
votes
If a unitary operator is close to the identity, will it leave any state it acts on unchanged?
Here is a very simple lower bound for the fidelity, maybe this helps in addition to the existing answer:
Let $U=\exp(-i\delta G)$, then using Duhamel's formula one can show the inequality $|| \exp(A) …
- 482