All Questions
Tagged with definition hilbert-space
77
questions
0
votes
0
answers
30
views
Differences between energy level and end energy state [duplicate]
What is differences between energy level and end energy state in quantum mechanic?
Are they same?
Is the energy state same as the quantum state?
0
votes
2
answers
131
views
Question on Dirac notation with operator [closed]
What does $\langle\psi|A|\phi\rangle$ mean if $A$ is some operator like how does $A$ acts on these two vectors $\phi$ and $\psi$ and what is it equal to and also does $A$ act on both vectors or just ...
- 33
4
votes
2
answers
627
views
What is the difference between "cluster states" and "graph states"?
I wonder about the difference between the cluster state and the graph state.
I guess the only difference is the graph of the cluster state is limited to a two-dimensional square lattice
The concept of ...
- 51
0
votes
1
answer
364
views
Radial position operator
While trying to find the expectation value of the radial distance $r$ of an electron in hydrogen atom in ground state the expression is:
$$\begin{aligned}\langle r\rangle &=\langle n \ell m|r| n \...
- 1,270
1
vote
1
answer
513
views
Definition of a wave packet
In Shankar's QM book page 168, the author stated
a wave packet is any wave function with reasonably well-defined
position and momentum.
What does he mean by resonably well-defined position and ...
- 4,235
0
votes
0
answers
54
views
Inner product evaluation in QM
On wikipedia on the page for inner product it states that for any two $x,y$ in a vector space $V$ the inner product $(\cdot , \cdot)$ satisfies $(ax, y) = a(x,y)$ where $a\in\mathbb{C}$.
The inner ...
- 73
1
vote
1
answer
53
views
What does Leggett mean by quantum states like $|\psi\rangle=(a|\psi_1\rangle+b|\psi_2\rangle)^N$?
In his article (p. 1986) Legett uses the notation $|\psi\rangle=(a|\psi_1\rangle+b|\psi_2\rangle)^N$ to classify "macroscopic quantum phenomena". Does the "$^N$" mean "$\...
- 448
4
votes
3
answers
529
views
$\left\langle{\hat{O}}^\dagger\varphi\middle|\psi\right\rangle$ How do I act the operator in bra?
$$\left\langle\varphi\middle|\hat{O}\middle|\psi\right\rangle=\left\langle{\hat{O}}^\dagger\varphi\middle|\psi\right\rangle.$$
In above formula, I have confused what does mean $\left\langle{\hat{O}}^\...
- 75
1
vote
1
answer
441
views
What is the difference between an eigenfunction and a wavefunction?
This question is an additional point of clarification to my previous question about adding position and momentum eigenstates.
For simplicity, suppose I had a particle in an eigenstate of momentum, $|p\...
- 2,680
1
vote
1
answer
106
views
Action of permutation operator on other operators
I'm watching MIT 8.06 Quantum physics, lecture $23.2$ See for example [1] Particularly See $5:41$. It is shown that
$$P_{21}B(1)P^\dagger_{21}|u_i\rangle_1\otimes |u_j\rangle_2=|u_i\rangle_1\otimes |...
- 11.9k
5
votes
1
answer
443
views
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 ...
- 11.8k
1
vote
1
answer
182
views
Requirement of Jordan-Wigner string in creation operator on Fock state
Our lecture notes described the action of the particle creation operator on a fermionic Fock state:
$$c_l^\dagger |n_1 n_2...\rangle = (-1)^{\sum_{j=1}^{l-1}n_j}|n_1 n_2 ... n_l+1 ...\rangle.$$
I am ...
- 2,604
3
votes
1
answer
1k
views
What exactly is a Fock state?
I am a bit confused by the way a Fock state is defined and hope to find some clarification.
The Fock space is defined as the direct sum of all $n$-particle Hilbertspaces $H_i$
$$F = H_0 \oplus H_1 \...
- 387
0
votes
1
answer
116
views
Is this definition of the Fourier Transform of a quantum field operator rigorous?
Let there be a a quantum field operator $\hat\phi(t,\vec{x})$ which, because it acts (pointwise) on a separable Hilbert space, I expect I can write as
$$\hat\phi(t,\vec{x}) = \sum_n\sum_m\phi^n_m(t,\...
- 34
3
votes
3
answers
430
views
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 ...
- 1,270