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Results tagged with hilbert-space
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user 154632
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.
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Expansion of an Eigenket
What is the purpose of multiplying only one base ket by $e^{i\theta}$, when expanding an eigenket as a linear combination of its base kets?
Example: $|S_x; +\rangle = \frac{1}{\sqrt2}(|+\rangle + |- …
- 243
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vote
2
answers
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Dirac Notation: Why are these two expressions equal?
Consider
$$
\langle a''|(AB - BA)|a' \rangle = (a'' - a') \langle a''|B|a' \rangle
$$
where $a''$ and $a'$ are eigenvalues of observable, $A$, which is Hermitian (real eigenvalues). $A$ and $B$ are …
- 243
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3
answers
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Bra Ket Notation and Derivative [duplicate]
Let $$a$$ be the partial derivative symbol with respect to $x$. What is $$\langle x|a|x \rangle$$ equal to? I think it is 0 but not sure.
- 243
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Partial Derivative and Dirac Notation [duplicate]
Does the partial derivative of $\langle x'|\alpha\rangle$ with respect to $x'$ equal $|\alpha\rangle$? Why?
Note: $|\alpha\rangle$ is an arbitrary ket, $x'$ is an eigenvalue, and $\langle x'|$ is an …
- 243