Linked Questions

10
votes
3answers
587 views

Is there a prediction of quantum mechanics that could be construed as representing an “energy-time uncertainty relation?” [duplicate]

As the title suggests. Is there a prediction of quantum mechanics that could be construed as representing an "energy-time uncertainty relation?" Does there exist any reference to such a prediction, or ...
1
vote
2answers
240 views

Interpretation of the energy-time uncertainty [duplicate]

From the uncertainty relation it follows that: $$\Delta E \ \Delta t = \hbar$$ $\Delta E$ is the energy uncertainty of a state, $\Delta t$ should be the uncertainty of the lifetime $\tau_b$ of the ...
1
vote
1answer
270 views

Time energy uncertainty principle [duplicate]

$ \sigma _{H}\sigma _{Q}\geqslant \frac{h}{4\pi }\frac{d\left \langle Q \right \rangle}{dt}$ $\Delta E = \sigma _{H}$ $\Delta t = \frac{\sigma _{Q}}{d\left \langle Q \right \rangle / dt}$ $\Delta E ...
1
vote
0answers
212 views

Virtual particles and Heisenberg's uncertainty principle [duplicate]

Introduction Virtual particles are particles which doesn't obey the energy–momentum relation: \begin{align}E^2=(mc^2)^2+(pc)^2\end{align}This is possible if it happens short enough time. Often ...
0
votes
1answer
62 views

Different statements of the Heisenberg uncertainty principle [duplicate]

I know that from the Heisenberg uncertainty principle, ∆x∆p=ℏ/2 . And I know that this equation can be rewritten as ∆t∆E=ℏ/2. From QED I also know that the equation ∆t∆E=ℏ/2 claims that some energy ...
-1
votes
2answers
87 views

Is energy always uncertain? [duplicate]

ΔE⋅Δt⩾ℏ/2 Does the energy time uncertainty principle imply that an object would have to stay for an infinite amount of time in a state for there to be no uncertainty in the energy of that state?
1
vote
0answers
77 views

Time-Energy Uncertainty [duplicate]

I can understand the Heisenberg Uncertainty Principle which states that $$\Delta{x}\Delta{p_x}\ge \hbar/2$$ I also understand that this can be extended to any canonical conjugates. But I can't seem to ...
0
votes
0answers
45 views

The Uncertainty Principle [duplicate]

We often say that the conservation of the energy could be violated by a quantity $\Delta E$ but only within a precise interval of time $\Delta t$, dictated by the Heisenberg principle ($\Delta t \...
0
votes
0answers
44 views

Energy - Time uncertainty relation [duplicate]

I have a question regarding the interpretation of the relation $\Delta E \Delta t \ge 1$. First, what is the exact meaning of $\Delta t$? We know that $\Delta E$ is calculated as the standard ...
0
votes
0answers
37 views

Definite energy in Quantum Mechanics [duplicate]

According to Phillips' "Introduction to Quantum Mechanics", Chapter 4 "an eigenfunction of the Hamiltonian always describes a state of definite energy". But how can that be without ...
1
vote
0answers
36 views

Energy-Time Uncertainty Relation and Virtual Particles [duplicate]

I've come across a hole in my understanding. Heisenberg's Uncertainty Principle can be expressed in terms of energy and time as $$ \Delta E \, \Delta t \geq \frac{\hbar}{2} $$ where $\Delta E$ is ...
0
votes
0answers
26 views

Does a quantum commutator exist for energy and time? [duplicate]

In quantum mechanics the position operator $\hat{x}$ and the momentum operator $\hat{p}$ have a commutator $$ [\hat{x}, \hat{p}] = i\hbar $$ Does a similar commutator also exist for the uncertainty ...
0
votes
0answers
18 views

Applying uncertainty principle to energy states [duplicate]

Often for this I have heard, the longer the lifetime of the energy state, the uncertainty in the energy state decreases as a result of heisenberg's uncertainty principle. However doesn't that look at ...
85
votes
14answers
13k 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 ...
96
votes
6answers
24k views

What is the physical meaning of commutators in quantum mechanics?

This is a question I've been asked several times by students and I tend to have a hard time phrasing it in terms they can understand. This is a natural question to ask and it is not usually well ...

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