The tag has no wiki summary.

learn more… | top users | synonyms

7
votes
6answers
1k views

What is an observer in quantum mechanics?

My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts. What is an observer? What are the conditions required to be qualified of observer, ...
14
votes
2answers
2k views

Time as a Hermitian operator in QM?

In non-relativistic QM, on one hand we have the following relations: $$\langle x | P | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial x} \psi(x),$$ $$\langle p | X | \psi \rangle ~=~ i \hbar ...
17
votes
3answers
2k views

How does non-commutativity lead to uncertainty?

I read that the non-commutativity of the quantum operators leads to the uncertainty principle. What I don't understand is how both things hang together. Is it that when you measure one thing first ...
4
votes
3answers
2k views

Why do we use Hermitian operators in QM?

Position, momentum, energy and other observables yield real-valued measurements. The Hilbert-space formalism accounts for this physical fact by associating observables with Hermitian ('self-adjoint') ...
14
votes
3answers
857 views

In what sense is a scalar field observable in QFT?

Consider a QFT consisting of a single, hermitian scalar field $\Phi$ on spacetime (say $\mathbb R^{3,1}$ for simplicity). At each point $x$ in spacetime, $\Phi(x)$ is an observable in the sense that ...
9
votes
5answers
11k views

What is the Physical Meaning of Commutation of Two Operators?

I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable ...
6
votes
8answers
1k views

What exactly is the 'observer' in physics and/or quantum mechanics? [duplicate]

Possible Duplicate: nature of an observer For instance, in the double slit experiment, what is exactly defined as an observer? I remember from somewhere, light is also an observer?
15
votes
1answer
702 views

Intuitive meaning of Hilbert Space formalism

I am totally confused about the Hilbert Space formalism of Quantum Mechanics. Can somebody please elaborate on the following points: The observables are given by self-adjoint operators on the ...
4
votes
2answers
396 views

Diff(M) and requirements on GR observables

This question is kind of inspired in this one: Diff(M) as a gauge group and local observables in theories with gravity The conundrum i'm trying to understand is how is derived the (quite) ...
6
votes
2answers
578 views

Eigenvalues of a quantum field?

Fields in classical mechanics are observables. For example, I can measure the value of the electric field at some (x,t). In quantum field theory, the classical field is promoted to an operator-valued ...
8
votes
1answer
748 views

“An operator is hermitian”. Implications?

Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter. The first part of his second postulate can be stated as: Every dynamical variable may be ...
4
votes
4answers
571 views

Is the wave function objective or subjective?

Here is a question I am curious about. Is the wave function objective or subjective, or is such a question meaningless? Conventionally, subjectivity is as follows: if a quantity is subjective then ...
3
votes
2answers
395 views

Uniqueness of eigenvector representation in a complete set of compatible observables

Sakurai states that if we have a complete, maximal set of compatible observables, say $A,B,C...$ Then, an eigenvector represented by $|a,b,c....>$, where $a,b,c...$ are respective eigenvalues, is ...
2
votes
3answers
151 views

What happens with a tunneling particle when its momentum is imaginary in QM?

In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to ...
17
votes
4answers
458 views

Is every quantum measurement reducible to measurements of position and time?

I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
11
votes
3answers
426 views

Is it possible to define a “it went through two slits” observable?

This concerns the famous two-slit experiment. Electrons or photons or your favorite particle, doesn't matter. As we all know, the attempt to detect which slit the quanta pass through leads to loss ...
6
votes
2answers
590 views

Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
5
votes
2answers
129 views

Inexact measurement and wavefunction collapse

As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is ...
2
votes
1answer
155 views

The Physical Meaning behind a Commutator [duplicate]

I've just been introduced to the idea of commutators and I'm aware that it's not a trivial thing if two operators $A$ and $B$ commute, i.e. if two Hermitian operators commute then the eigenvalues of ...
3
votes
2answers
139 views

Understanding Well Defined States

I am self-studying from a text in QM. Well defined states are mentioned several times. By and large these are consistent and seem to be readily apparent: states of well defined energy are basis ...
2
votes
1answer
172 views

What are the Time Operators in Quantum Mechanics? [duplicate]

I don't understand at all what the time operators are in quantum mechanics. I thought that given a wave function, because it's a function of time, we could simple put in any time in the future to find ...
4
votes
2answers
233 views

Uniqueness of eigenvector representation in a complete set of compatible observables [duplicate]

Possible Duplicate: Uniqueness of eigenvector representation in a complete set of compatible observables Sakurai states that if we have a complete, maximal set of compatible observables, ...
2
votes
1answer
172 views

Non-Hermitian operator with real eigenvalues?

So we know that in Quantum Mechanics we require the operators to be Hermitian, so that their eigenvalues are real ($\in \mathbb{R}$) because they correspond to observables. What about a non-Hermitian ...
1
vote
2answers
264 views

Can we measure “wavefunction” of quantum particles?

We know that there is uncertainty principle, so question: can we ever measure wavefunction of particles? I do not think this is possible, but I am not sure. I guess that everything is probabilistic. ...
0
votes
1answer
56 views

Discrete Values for Observables vs Average Values (Quantum Mechanics)

When considering observables and their corresponding operators, would it be correct to believe that discerning discrete values for an observable is possible ONLY when $\psi$ is an eigenfunction of the ...
0
votes
3answers
432 views

Why is $\int (dp/2\pi) |p \rangle\langle p| = 1 $?

In quantum mechanics, why is $\int (dp/2\pi) |p \rangle\langle p| = 1 $ where $|p \rangle$ represents momentum eigenstate?