All Questions
Tagged with definition hilbert-space
77
questions
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Clarification in the difference between metastable states and excited states
The answer of this question What is the difference between metastable states and excited states?
is that the difference lie in the the time that the systems lie in a given state.
So for example take ...
- 445
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1
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What is the difference between metastable states and excited states?
In the book Mathematical concepts of quantum mechanics ,Stephen J. Gustafson Israel,Michael Sigal, they say
The notion of a resonance is a key notion in quantum physics. It
refers to a metastable ...
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14
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1
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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
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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 $\ell$ ...
8
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3
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Equivalent definitions of total angular momentum
Consider the equality
\begin{equation}\exp\left(-\frac{i}{\hbar}\boldsymbol{\phi J}\right)\left|x\right>=\left|R(\phi)x\right>,\end{equation}
where $\left|x\right>$ denotes a position ...
user224659
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154
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Off-shell vs half off-shell vs fully off-shell $T$-matrix
I know what are on-shell particles, but I want to know what are off-shell, and half off-shell, and fully off-shell states? and how we decide to consider one of these states in evaluating $T$-Matrix?
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2
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2
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680
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What is a pseudopure state?
In the paper titled "Experimental Implementation of the Quantum Baker’s Map" by Weinstein et al. (Phys. Rev. Let. 89 (2002)), the author says something like
[...] the pseudopure state corresponding ...
- 2,283
3
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3
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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 ...
- 201
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Does the set of the degenerated eigenfunctions of hamiltonian forms a subspace?
I have read in a book that the set $\{ \Psi_{n}^{(\nu)} \in \mathcal{H} | \ \ \hat{H}\Psi_{n}^{(\nu)} = E_{n}\Psi_{n}^{(\nu)} \}$ (that is, the set of all eigenfunctions of the hamiltonian with the ...
- 587
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432
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Precise definition of the Hilbert space in QM?
In QM books (at least those I have read) the definition of the Hilbert space used is somewhat blurred (the "space of square integrable functions" is not enough to define it precisely : which kind of ...
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698
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Is a bound state a stationary state?
In Shankar's discussion on the 1D infinite square well in Principles of Quantum Mechanics (2nd edition), he made the following statement:
Now $\langle P \rangle = 0$ in any bound state for the ...
- 325
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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 \...
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418
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Difference between pure and thermal states
As far as I know by inserting a harmonic potential $V(x) = \frac{1}{2}m \omega x^2$ into the time-independent schrödinger equation I can obtain the wave-functions eigenstates and eigenvalues (energies)...
- 415
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Ladder operators vs creation/annihilation operators
I am trying to figure out the difference between the ladder operators (for harmonic oscillator) $a^\dagger$, $a$ and the creating/annihilation operators $c^\dagger$, $c$. Are they the same? I have ...
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Tracing over a Fock space?
Suppose you have a bosonic Fock space with a vacuum $|0\rangle$. A particular state is labeled by the parameter $N \in \mathbb{Z}$. You can construct states like
$$
| n_{N} \rangle = \frac{ \left( \...
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