All Questions
Tagged with definition hilbert-space
77
questions
0
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1
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107
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Mathematical meaning of a position eigenbra $\langle x_0 |$
Let $|x_0\rangle$ be an position eigenket. The physical picture I have for $|x_0\rangle$ is a particle located at $x_0$. Thus it should be represented by a delta function $\delta(x-x_0)$.
For $f\in L^...
- 3,350
5
votes
2
answers
4k
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What does it mean when a degeneracy is lifted?
I would like to ask what is the meaning of degeneracy been lifted? For example when the Schrodinger equation is subjected to magnetic field, there is a $m\ell$ degeneracy is lifted while $\ell$ ...
- 35.4k
1
vote
1
answer
75
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Difference between stationary states, collision states, scattering states, and bound states
A few weeks ago, I was presented one-dimensional systems in my QM class, and of course one-dimensional potentials too. Nonetheless, I'm still a bit unclear about the terminology my professor uses. ...
- 207k
1
vote
2
answers
3k
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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.
- 207k
-1
votes
2
answers
99
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Are Hermitian operators Hermitian in any basis? [closed]
Given a Hilbert space and a Hermitian operator defined on it, will the operator exhibit Hermiticity in any basis used to span the space? My thought on this is that this must be the case, after all, if ...
- 207k
0
votes
1
answer
79
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What is the difference between $(\mathcal{H}\setminus \{ 0\})/\mathbb{C}^*$ and $\mathcal{H}_1/U(1)$?
Let $\mathcal{H}$ be a Hilbert space. We define the projective Hilbert space $\mathbb{P}\mathcal{H}$ as $\mathcal{H}\setminus \{ 0\}/\mathbb{C}^*$. Then $[\Psi]=\{ z\Psi :z\in \mathbb{C}^*\}$.
On the ...
- 207k
3
votes
3
answers
3k
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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 ...
- 207k
3
votes
3
answers
430
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Understanding the bra-ket antilinear correspondence
I can't follow how the above argument leads to (1.8).
I am able to prove it only if I can show $$\langle a | c\rangle+\langle b| c\rangle=(\langle a|+\langle b|)\,|c\rangle$$
But I don't understand ...
- 2,075
2
votes
0
answers
115
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What is the definition of bound state in quantum field theory?
I asked a question a while a go what is a bound state and the question was closed because there is a similar question.
Now since best description we have to describe nature in quantum field theory
How ...
- 207k
2
votes
2
answers
1k
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Physical meaning of Transpose of an Operator in Quantum Mechanics?
What's the physical meaning of transpose of a matrix in Quantum Mechanics?
Although for Unitary or Orthogonal operators, I know that transpose of that operator would reverse the action and that's ...
CommunityBot
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-2
votes
1
answer
144
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What is meant by " a basis is diagonal"?
I am trying to understand Schmidt decomposition. I am stuck in one sentence here. See the example picture.
Here, I can understand everything except the line "For both
HA and HB the Schmidt basis ...
- 1,417
1
vote
4
answers
512
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What actually is superposition?
What does superposition actually mean? Can something like an atom actually be in two different states at once or do we just not know which state it is in? Also, how can our act of observing something ...
- 50.2k
1
vote
2
answers
1k
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Tensor Product vs Direct Product in QM
Consider adding angular momentum. Shankar describes the state of the system as the direct product of states while Ballentine (and I think most other people) describes the state of the system as the ...
- 64.2k
1
vote
1
answer
120
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What is the definition of a stationary state?
In this answer, a state, $\psi(t)$ is said to be stationary if
$$
\begin{equation*}
|\psi(t)|^2=|\psi(0)|^2.
\end{equation*}
$$
That answer then concludes that a state can only be stationary if it is ...
- 207k
1
vote
1
answer
132
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A theorem about functions of self-adjoint operators
It is very common (see e.g. page 18 of Ballentine's Quantum Mechanics: A Modern Development) for the following development to take place. We couch the discussion in Dirac's bra-ket notation noting ...
- 207k