All Questions
Tagged with definition hilbert-space
77
questions
12
votes
3
answers
2k
views
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, ...
- 131
5
votes
4
answers
3k
views
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 ...
- 297
2
votes
3
answers
813
views
Why is a null field also primary, in CFT?
I do not understand how to prove the statement, mentioned in pag 205 of Di Francesco's book "Conformal Field Theory":
Let $|\chi\rangle$ be a null vector, i.e. such that $L_n |\chi\rangle = 0$ for $n&...
- 2,060
-2
votes
1
answer
89
views
What is meant by Projected Hilbert space?
What is meant by Projected Hilbert space? I know almost everything about coherent states. But I don't know the use of projected coherent states. I googled, but I can't find any source.
- 29
8
votes
3
answers
2k
views
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 $\...
- 36.4k
1
vote
0
answers
353
views
Hermitian and Self-adjoint Operators [duplicate]
I was wondering what the mathematical distinction between Hermitian and self-adjoint operators were in the context of quantum mechanics? Most texts use this paradigm interchangeably.
- 43
1
vote
2
answers
3k
views
Differences between eigenstates, bound states and stationary states [closed]
I am not very clear about the differences between eigenstates, bound states and stationary states.
- 27
31
votes
5
answers
12k
views
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 ...
4
votes
3
answers
597
views
Why does Griffiths define the complex inner product differently? [closed]
I have just now noticed that Griffiths (in his book Introduction to Quantum Mechanics) defines the complex inner product as
$$\big<z,w\big>~=~\sum_{i=1}^n\overline{z}_iw_i.$$
In all ...
- 236
3
votes
1
answer
2k
views
Hermitian Adjoint of Spinor
Say we have a four component spinor $\psi$:
$$
\psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix}
$$
Is the Hermitian adjoint of this:
$$
\psi^\dagger =\begin{pmatrix}\psi_L^\dagger \psi_R^\dagger\end{...
user77345
42
votes
5
answers
8k
views
Hilbert space vs. Projective Hilbert space
Hilbert space and rays:
In a very general sense, we say that quantum states of a quantum mechanical system correspond to rays in the Hilbert space $\mathcal{H}$, such that for any $c∈ℂ$ the state $\...
- 4,685
2
votes
1
answer
517
views
What is many-body bound state?
Bound state by definition is a state when particles are bounded together, so then "many-body bound state" would be bound state for a system of many bodies. Then I have several puzzles:
is the state ...
- 225
12
votes
4
answers
9k
views
How is a bound state defined in quantum mechanics?
How is a bound state defined in quantum mechanics for states which are not eigenstates of the Hamiltonian i.e. which do not have definite energies? Can a superposition state like $$\psi(x,t)=\frac{1}{\...
- 26.8k
21
votes
1
answer
5k
views
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 ...
- 415
2
votes
2
answers
13k
views
Definition of "localized state"
Is there a definition of a localized state in quantum mechanics? I've seen that some textbooks use this term, but they don't give a definition.
- 3,732