17
votes
Accepted
"There is a bra for every ket, but there is not a ket for every bra"
The kets and bras do not always live in a Hilbert space, but when you write something like the "position eigenbras" $\langle x\rvert$, this lives in a larger space that is part of the Gel'...
- 127k
13
votes
Accepted
Which operators do non-invertible symmetries correspond to in quantum mechanics?
What is a non-invertible symmetry?
You already know what a local operator is: $\phi(x)$ is local because its support is a point $x$. You also know what a line operator is: for example, a Wilson line $...
12
votes
Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
The thrust of Bell's Theorem is that any classical random variables (which, by definition, satisfy the Kolmogorov axioms) have to satisfy certain inequalities. Some quantum mechanical observables ...
- 16.4k
11
votes
Accepted
Understanding the parabolic state of a quantum particle in the infinite square well
Before we can answer the question, we need a little bit more mathematical clarity here. However, we won't be fully rigorous and leave out details which are not of interest for the question.$^\ddagger$
...
- 8,375
11
votes
Accepted
Conservation of the determinant of density matrix
The determinant is the product of the eigenvalues. It is thus preserved under any unitary evolution (such as the one given by the Schrödinger equation). This holds independent of the dimension of the ...
- 21.1k
8
votes
Accepted
Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
(ADDED 9/16: My much longer response, explaining why there are no "local nonrealistic" models of entanglement, can now be found in this related recent question.)
original response:
You are ...
- 1,959
8
votes
Wrong explanation for why "electron can't exist in the nucleus"?
When are asked about why an electron cannot fall into the nucleus...
This is a common "problem" when talking about the issues with the classical picture of an electron orbiting the nucleus, ...
- 58.3k
7
votes
Accepted
Doubt about dirac notation
By definition
$$
X |x\rangle = x | x \rangle , \qquad X | -x\rangle = (-x)|-x\rangle
$$
Suppose that $|-x\rangle = - |x\rangle$. Acting on both sides with $X$, we then have
$$
X |-x\rangle = - X |x\...
- 27.1k
7
votes
Wrong explanation for why "electron can't exist in the nucleus"?
Electrons do "spend time" inside the nucleus, just as they "spend time" in other spherical regions of a similar size. You can see that from the fact that the $1s$ orbital wave ...
- 28.3k
7
votes
Understanding the parabolic state of a quantum particle in the infinite square well
There's a simple error in your $\psi_n$ which is screwing you up. In general, the form of the eigenstates $\psi_n(x;x_o,L)$ for a well of length $L$ starting at $x_o$ is
$$
\psi_n(x;x_o,L) \propto \...
- 902
7
votes
Accepted
Interpretation of the ideal gas single particle partition function
In fact, it is not clear why one can assume that $V/\Lambda^3$ is equal to the average number of particles that can fit into a volume $V$. What is the distribution of the number of particles from ...
- 6,095
6
votes
Are quantum measurements on two different particles always commutative?
Yes, they commute. However, it's not correct to talk about the commutator $[A,B]$ because these are operators defined on different Hilbert spaces.
When you have a system of two particles, the state of ...
- 81
6
votes
Accepted
Unperturbed Green's Function for an electron in an empty band
Because that "physicist's argument" is, well, wrong. Whenever your teacher invoked the argument, they secretly sneaked in the $i \delta$ without telling you. Younger kids are sometimes ...
- 442
5
votes
Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
It is often said that the Bell test disqualifies "local realistic"
theories from quantum physics.
This implies that there are 3 out of 4 classes of theories from the following list, that ...
- 7,686
5
votes
Wrong explanation for why "electron can't exist in the nucleus"?
Everything @BioPhysicist is correct, but in addition:
Your argument is semi-classical, quantum mechanics is non-relativistic (there is no $c$ in the Schrödinger Eq.), and the problem involves ...
- 37.1k
5
votes
Understanding the parabolic state of a quantum particle in the infinite square well
Barring the (now corrected) mistake of the omission of part of eigenvectors,
the point is quite trivial: here one is referring to two different notions of energy observable but using the same name!
...
- 75.8k
5
votes
Quantum behavior of small atoms and molecules in a material
It is definitely not true that molecules behave in accordance with classical physics at room temperature.
I will give the most traditional example, which can be found in Chapter 40 of the Feynman ...
- 1,781
5
votes
Accepted
Does measuring a quantum object collapse the wave function even if the particle is not found in the position where it was measured?
The "collapse of the wave function" is a very unphysical concept: It was invented within the Copenhagen Interpretation by people who tried to make sense of Quantum Mechanics, and who ...
5
votes
Comparing force-carrying particles
There's different levels of sophistication you could give to this question, but at the most basic level: empirically, general relativity is an extremely successful theory of gravity and agrees with ...
- 52.5k
4
votes
Accepted
Does the collapse axiom predict non-physical states in the case of measurement of continuous-spectrum quantities?
Since my name directly appears in the question, I think that I should try to answer. Also because I substantially changed some ideas about some of these issues in the last years.
First of all, the ...
- 75.8k
4
votes
How can non-realism alone explain quantum entanglement?
After two recent questions on this (here's the other one), I felt it was time to write up a long account on why there are no “local non-realist” theories which can explain Bell Correlations. (A few ...
- 1,959
4
votes
Understanding the parabolic state of a quantum particle in the infinite square well
Let's be clearer with the essence of your problem, now that the other answerer brought to your attention that you were missing the cosines.
Your state is $\left<x|\psi\right>=\sqrt{\frac{15}{16\...
- 10.4k
4
votes
Accepted
When a function of the position operator is self-adjoint?
Necessary and sufficient conditions on $f: \mathbb{R} \to \mathbb{C}$ to make $f(A)$ selfadjoint if $A$ is selfadjoint (generally unbounded and defined in a dense domain) are that both
(a) $f$ is real ...
- 75.8k
4
votes
How can events on the quantum-level be random but not on the macro-level?
All models are wrong; some are useful
"How science is explained" is really a topic for the math & science educators stack exchange. But if you want to look at what scientists really ...
- 50.8k
4
votes
Explicit Expression of $S_2(\zeta)$ on a general Fock State?
The operators $\hat a\hat b\sim K_-$ and $\hat a^\dagger \hat b^\dagger\sim K_+$ are ladder operators of the $su(1,1)$ algebra so one possibility is to use the $SU(1,1)$ disentanglement formula
$$
D(\...
- 46.9k
4
votes
Conservation of the determinant of density matrix
The density matrix for a $2\times 2$ system can be written as a linear combination of the identity and the Pauli matrices:
$$
\rho= \frac12 \left(I+\boldsymbol{P}\cdot\boldsymbol{\sigma}\right)
$$
...
- 46.9k
4
votes
Accepted
What' the intuition behind Shankar's postulate II?
In classical physics the evolution of the position and momentum of a particle are described by functions $x(t),p(t)$ whose values are the value you would get if you measured the position and momentum ...
- 9,308
4
votes
Can a hypothetically massless object/particle of finite size spin around its own center in a fixed position in space?
What you are describing is physically impossible.
Massless fundamental particles exist, like photons and gluons, and indeed they have a spin though this is a quantum mechanical property and not ...
- 360k
3
votes
Interpretation of the ideal gas single particle partition function
Here comes the part that troubles me. How can the """number of particles that can fit on average in the real space volume"""" be related to the number of states ?
...
- 62k
3
votes
Comparing force-carrying particles
From a theoretical point of view you can see this as the fact that the 3 standard model interactions are forces (they generate 1D displacements), while in general relativity gravity exerts ...
- 1,809
Only top scored, non community-wiki answers of a minimum length are eligible