All Questions
Tagged with definition hilbert-space
16
questions
9
votes
3
answers
4k
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What is quantum entanglement? [closed]
What is quantum entanglement?
Please be pedagogical.
Edit: I have updated my background under my profile.
- 455
42
votes
5
answers
8k
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Hilbert space vs. Projective Hilbert space
Hilbert space and rays:
In a very general sense, we say that quantum states of a quantum mechanical system correspond to rays in the Hilbert space $\mathcal{H}$, such that for any $c∈ℂ$ the state $\...
- 4,685
21
votes
1
answer
5k
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Unitary quantum field theory
What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one ...
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8
votes
2
answers
677
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Are all bound states normalizeable?
Following Griffiths eq. (2.91) on p. 52 one may define a bound state to be an energy eigenstate
$$H|E\rangle=E|E\rangle\tag{1}$$
with an energy being smaller than the potential far away from the ...
user224659
2
votes
3
answers
723
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Confused about definition of three dimensional position operator in QM
My QM text defines the position operator as follows:
The position operator $X= (X_1,X_2,X_3)$ is such that for $j=1,2,3: \ X_j \psi(x,y,z)= x_j \psi(x,y,z)$.
To me this can mean two things.
1) $...
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31
votes
5
answers
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What is a state in physics?
What is a state in physics? While reading physics, I have heard many a times a "___" system is in "____" state but the definition of a state was never provided (and googling brings me totally ...
18
votes
2
answers
4k
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What is a coherent state?
In quantum mechanics, what exactly is a coherent state, and how does it differ from other states?
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14
votes
1
answer
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Difference between Fock space and Hilbert Space
I am beginner in QFT. I would like to know why there is a need of constructing Fock space for a $N$-particle system? Why can't we represent this many body system just as the tensor product of Hilbert ...
- 1,348
12
votes
4
answers
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How is a bound state defined in quantum mechanics?
How is a bound state defined in quantum mechanics for states which are not eigenstates of the Hamiltonian i.e. which do not have definite energies? Can a superposition state like $$\psi(x,t)=\frac{1}{\...
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8
votes
3
answers
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Intuition on the GNS construction and how it relates to usual quantum mechanics
Reading one paper, the GNS construction is mentioned as follows:
It is important to recall that a result (theorem) due to Gel'fand, Naimark and Segal (GNS) establishes that for any $\omega$ on $\...
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6
votes
1
answer
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Definition of the $S$-Matrix in Schwartz QFT-Book: Why is $\langle f, t_f | i, t_i \rangle$ in the Schroedinger picture, and not Heisenberg-picture?
On page 51, (equation 5.1), Mathew Schwartz introduces the $S$-matrix as
\begin{align}
\langle f| S | i \rangle_{Heisenberg} = \langle f, \infty | i, -\infty \rangle_{Schrödinger}
\end{align}
Were $|i,...
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5
votes
1
answer
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What is a quasibound state and how is it different from a bound state?
What is a quasibound state and how is it different from a bound state?
I have read this term in nuclear physics in the context of compound nucleus formation. A compound nucleus $C$ is formed by the ...
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4
votes
2
answers
208
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Mathematical formulation of quantum mechanics
I am reading a book on quantum mechanics, but it is difficult to understand.
Quantum mechanics is roughly formulated as follows:
Physicsl state is a normalized ray $\{e^{i\theta}\psi|\theta \in \...
- 41
3
votes
3
answers
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Is there a difference between a Hermitian operator and an observable? [duplicate]
My poorly written lecture notes say that any Hermitian operator does have a complete set of orthogonal eigenstates with real corresponding eigenvalues and is therefore an observable.
In the article ...
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1
vote
2
answers
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Differences between eigenstates, bound states and stationary states [closed]
I am not very clear about the differences between eigenstates, bound states and stationary states.
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