Questions tagged [hilbert-space]
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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Super Hilbert space of SYM
I hope this message finds you well. I am currently try to understand explicitly, at least in some sense, $d=4$, ${\cal N}=4$ super Yang-Mills theory.
What is the explicit construction of the super ...
- 11
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Diagonalizing the Hamiltonian in plane wave basis to solve the finite square well doesn't work properly [closed]
The potential for a finite well is given by
$$
\begin{equation}
V(x) = \begin{cases}
0,\,&|x|> a\\
-V_0,\,&|x|\leq a
\end{cases}
\end{equation}
$$
I try to determine ...
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How do operators on kets and wavefunctions correspond?
Let $\hat{A}$ be an operator on Hilbert space vectors. How does one show that there always exists a corresponding operator $\hat{a}$ on wave functions? i.e. $\exists \hat{a}:L^2\rightarrow L^2$ s.t. $$...
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Some confusion about understanding the relativistic quantum mechanics
S. Weinberg in his book "The quantum theory of fields" chapter 2 introduced the notion of symmetry in quantum mechanic as follows: Physical states are represented by rays in Hilbert space. ...
- 374
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Dirac's Bracket Notation
I have a question on Dirac's bracket notation. In particular, according to this notation, vectors and covectors are represented by $|\psi\rangle$ and $\langle\psi|$ respectively. Moreover, these two ...
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What kind of law can accurately describe atomic nuclei? [closed]
I understand that atomic nuclei are much too dense to behave as an ideal gas. Are they degenerate? I would assume so (similar to neutron stars), but couldn't find any laws that would accurately ...
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Do optimal Lieb-Thirring constants have physical meaning?
In their proof of stability of matter Lieb and Thirring used a particular set of inequalities. Namely, if $H=-\Delta+V(x)$ is a Schrödinger operator, then the sum of (powers of the absolute value of) ...
- 131
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Kramer's degeneracy and ambiguity in time-reversal operator
To my understanding, time reversal symmetry can be represented by an anti-linear operator $T=U\mathcal{K}$, where $U$ is a unitary operator and $\mathcal{K}$ represents complex conjugation. This ...
- 503
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2
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Operator's definition in Dirac picture [closed]
I have a question about the definition of quantum operators in the Dirac picture. The definition is: $$A=\sum_i \sum_j \vert i \rangle A_{ij} \langle j \vert.\tag{1}$$
By deplacing the ket vector I ...
- 41
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2
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90
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The eigenvectors associated to the continuous spectrum in Dirac formalism
I am comfused about the definition of an observable, eigenvectors and the spectrum in the physics litterature. All what I did understand from Dirac's monograph is that the state space is a complex ...
- 173
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The meaning of a representation in one-dimensional quantum mechanics
In many places, one reads about chosing a representation for studying a particular one-dimensional quantum system. Usual representations are the position representation, the momentum representation or ...
- 173
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About momentum states covariant normalization
I'm following QFT of Schwrtz and I have a doubt about Eq. (2.72).
In particular, from Eq. (2.69): $$[a_k,a_p^\dagger]=(2\pi)^3\delta^3(\vec{p}-\vec{k}),\tag{2.69}$$ and Eq. (2.70): $$a_p^\dagger|0\...
- 147
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What is the dimension considered in the Schmidt Decomposition?
In the Schmidt decomposition, is the dimension considered of each Hilbert space the complex or real one? Meaning the complex dimension of $\mathbb C^2$ has dimension $2$, not $4$. If so when you ...
- 139
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Quantum: why linear combination of vectors (superposition) is described as "both at the same time"?
I want to get a better understanding of quantum phenomena and out world in general. Before long I've thought of Schrödinger cat as being both alive and dead (or spin both up and down). Now after some ...
- 516
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Asymptotic states and physical states in QFT scattering theory
Context
In the scattering theory of QFT, one may impose the asymptotic conditions on the field:
\begin{align}
\lim_{t\to\pm\infty} \langle \alpha | \hat{\phi}(t,\mathbf{x}) | \beta \rangle = \sqrt{Z} \...
- 108