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Results tagged with hilbert-space
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user 250506
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.
0
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What does it mean to expand a function in its basis?
From a physical point of view, you are always interested in observables, which you describe quantum mechanically by means of some hermitian operator. In fact, a property of Hermitian operators is havi …
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3
votes
Accepted
Strange use of the mean value into the definition of operators
What is meant by that expression is
$\Delta\hat{x}=\hat{x}-\langle\hat{x}\rangle \text{Id}$,
with $\text{Id}$ being the identity operator.
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5
votes
Operator norm and Action
The sup in the equation is a supremum over all states out of the Hilbert space $\mathcal{H}$. In other words, you pick the state $|\psi\rangle$ out of $\mathcal{H}$ for which the number $\frac{\mid\mi …
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2
votes
Accepted
Understanding Dirac notation from matrix representation
Given that $O_{ij}$ is the entry of the matrix $O$ at the $i$-th row and $j$-th column, the operator $\hat{O}$, from which you obtain the matrix $O$ by projecting it on elements $|i\rangle$ and $|j\ra …
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2
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Why does Quantum Mechanics use Linear Algebra?
If you want to study quantum mechanics, keep on working on linear algebra and try to really understand it. To put it short, you describe a quantum mechanical system using a state $|\psi\rangle$, which …
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