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Results tagged with hilbert-space
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user 94467
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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Understanding of bosons and fermions from time-dependent state in Srednicki's QFT
Recently, I am reading Srednicke's QFT by myself and just get started. In the very beginning chapter Attempts at Relativistic Quantum Mechanics, it says that consider a time-dependent state of the for …
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Understanding of bosons and fermions from time-dependent state in Srednicki's QFT
According to user487344's idea. For each arbitrary pair of $x_i$ and $x_j$, the function after doing the integral of all $x_k$ except $x_i$ and $x_j$ can only leave its symmetric part, say the followi …
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Quantum Field Theory Interpretation of $\hat{\phi}|0\rangle$ [duplicate]
Recently, I am reading the Tong's note of QFT. I have 2 question.
In the note, $\hat{\phi}(x)|0\rangle:=|x\rangle$ being interpreted as creating a particle in spacetime $(x^0,\vec{x})$. It is quite …
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Proof an infinite dimensional/continous completeness relation $\int|x\rangle \langle x| dx=1$
My question is how to prove
$$\int|x\rangle \langle x| dx=1$$
where $|x\rangle$ is a eigenstate of a self-adjoint operator $X$ whose spectrum is continuous?
I want to have a rigorous mathematical pro …
- 431
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QM question of the $z$ Matrix element in Angular Momentum Basis
I found a quite challenge quantum mechanics problem in a preparation sample test for a midterm.
Consider an electron moving in a central potential. Suppose that we know the matrix element of the …
- 431