All Questions
Tagged with definition hilbert-space
77
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42
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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 $\...
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votes
5
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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 ...
21
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1
answer
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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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answers
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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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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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3
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Definition of an operator in quantum mechanics
In J.J. Sakurai's Modern Quantum Mechanics, the same operator $X$ acts on both, elements of the ket space and the bra space to produce elements of the ket and bra space, respectively. Mathematically, ...
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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 $$\psi(x,t)=\frac{1}{\...
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What is quantum entanglement? [closed]
What is quantum entanglement?
Please be pedagogical.
Edit: I have updated my background under my profile.
- 455
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2
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Are all bound states normalizeable?
Following Griffiths eq. (2.91) on p. 52 one may define a bound state to be an energy eigenstate
$$H|E\rangle=E|E\rangle\tag{1}$$
with an energy being smaller than the potential far away from the ...
user224659
8
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3
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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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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
7
votes
1
answer
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Why do self-adjoint operators have to be densely defined?
I have been watching the Schiller lectures on QM and have been going through ‘quantum mechanics and quantum field theory’ by Dimock.
Both seem to ensure operators are densely defined, especially if ...
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6
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1
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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,...
- 6,763
6
votes
1
answer
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Correspondence between mathematician's and physicist's vertex operator algebra (VOA)
I have some conceptual doubts to clear up, in terms of piecing together what we learn of a vertex operator algebra (VOA) in conformal field theory, and how it is defined by a mathematician, say from ...
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Difference between pure quantum states and coherent quantum states
In the post What is coherence in quantum mechanics? and the answer by udrv in this post it seems to imply that a pure quantum state and coherent quantum state are the same thing since any pure state ...
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