Linked Questions
27 questions linked to/from Is there a time operator in quantum mechanics?
0
votes
1
answer
841
views
Relativistic Commutation relation for momentum and position [duplicate]
We all know that the canonical commutation relation give you
$$[x^i,p_j]=i\hbar~\delta^i_j,\qquad i,j=1,2,3.$$
Is there a relativistic version such as
$$[x^a,p_b]=i\hbar~\delta_b^a,\qquad a,b=0,...
- 1,231
121
votes
15
answers
20k
views
Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?
In the time-dependent Schrodinger equation, $ H\Psi = i\hbar\frac{\partial}{\partial t}\Psi,$ the Hamiltonian operator is given by
$$\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V.$$
Why can't we ...
- 17.3k
34
votes
3
answers
10k
views
Time as a Hermitian operator in quantum mechanics
In non-relativistic QM, on one hand we have the following relations:
$$\langle x | P | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial x} \psi(x),$$
$$\langle p | X | \psi \rangle ~=~ i \hbar \...
- 1,515
23
votes
4
answers
16k
views
Does the uncertainty principle apply to photons?
Wikipedia claims the following:
More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons. Being massless, they cannot be localized without being ...
- 3,688
32
votes
3
answers
7k
views
Is there an actual proof for the energy-time Uncertainty Principle?
As I understand, the energy-time uncertainty principle can't be derived from the generalized uncertainty relation. This is because time is a dynamical variable and not an observable in the same sense ...
- 7,860
14
votes
2
answers
5k
views
Position operator in QFT
My Professor in QFT did a move which I cannot follow:
Given the state $$\hat\phi|0\rangle = \int \frac{d^3p}{(2\pi)^3 2 E_p} a^\dagger_p e^{- i p_\mu x^\mu}|0\rangle,$$ he wanted to show that this ...
- 263
3
votes
1
answer
3k
views
Why isn't the time-derivative considered an operator in quantum mechanics? [duplicate]
Based on my understanding when doing quantum mechanics we deal with a small set of mathematical objects: namely scalars, kets, bras, and operators. But then in the Schrodinger equation we have this ...
- 5,369
3
votes
4
answers
446
views
What possible variants/permutations/derivatives are there of the Heisenberg uncertainty principle?
Generally, the (Heisenberg) uncertainty principle is stated as:
$\Delta x \cdot \Delta p \geq \dfrac{\hbar}{2}$
But sometimes you also encounter a variant of it, placing limits on other entities, such ...
- 561
4
votes
2
answers
6k
views
Is there an observable of time? [duplicate]
In Quantum Mechanics, position is an observable, but time may be not. I think that time is simply a classical parameter associated with the act of measurement, but is there an observable of time? And ...
2
votes
1
answer
3k
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 ...
user24082
6
votes
2
answers
770
views
Is there a natural operator that is canonically conjugate to the Hamiltonian?
As is well known, the Heisenberg uncertainty principle states that the position and momentum satisfy an uncertainty relation, which follows from the canonical commutation relation
\begin{equation}
[\...
- 290
3
votes
2
answers
1k
views
Time in special relativity and quantum mechanics
The time is treated differently in special relativity and quantum mechanics. What is the exact difference and why relativistic quantum mechanics (Dirac equation etc.) works?
- 2,176
11
votes
2
answers
962
views
How is quantum entanglement consistent with the relativity of time?
It is well known that relativity predicts time moves slowly near massive objects e.g.. time moves slowly for clocks on earth as compared to clocks on GPS satellites by about 40000 nanoseconds.
...
- 2,803
1
vote
1
answer
820
views
Why don't expectation values for a stationary state evolve over time?
I have an observable $O$ with operator $\hat{O}$. $\Psi_1$ is a wave function in an energy eigenstate, and $\psi_1$ is the corresponding spatial wave function. $E$ is the corresponding energy.
It is ...
- 11
5
votes
2
answers
604
views
Why isn't the Heisenberg uncertainty principle stated in terms of spacetime?
As I understand it, there are two "versions" of the Heisenberg uncertainty principle:
Position-Momentum uncertainty
\begin{equation}
\sigma_x \sigma_p \geq \frac{\hbar}{2}
\end{equation}
where $[...
- 4,231