[Q] Time uncertainty and particle energy similar to photon

In summary, the conversation discusses the application of the operator "i\hbar \frac{\partial}{\partial x}" to an energy eigenstate that evolves in time. This results in an energy eigenvalue of " \hbar w" that is analogous to the energy of a photon. The speaker is surprised by this relationship and wonders how it can happen. They also question whether the electromagnetic field is an energy eigenstate of a photon. The second question concerns the result " [i\hbar \frac{\partial}{\partial x},t] = \hbar^2" and the corresponding uncertainty " \Delta E \Delta t \geq \frac{\hbar}{2}". The speaker wonders about the meaning of
  • #1
good_phy
45
0
Hi i applied [itex] i\hbar \frac{\partial}{\partial x} [/itex] to energy eigen state which is

evolving in time, [itex] e^{(i(kx-wt)} [/itex] and i get energy eigen value [itex] \hbar w

[/itex]

but i was surprised it is very analoguos to energy of photon!

How can is it happened? Energy of photon is depending on time frequency of

electormagnetic field and Every of free particle is depending on time frequency of its energy

eigen state in time evolution.

Even i thought electromagnetic field is energy eigen state of photon. Is it right?


And i have second question about result [itex] [i\hbar \frac{\partial}{\partial x},t] = \hbar^2 [/itex] and corresponding uncertainty [itex] \Delta E \Delta t \geq \frac{\hbar}{2} [/itex]

What does means time uncertainty? time for what? We are not able to determine exact time

current state is in? we can't conclude t of [itex] e^{(i(kx-wt)} [/itex] ?
 
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  • #2
I think the dispersion relation is different. For a photon w~k, but for a massive particle w~k2, because the Hamiltonian contains the second derivative of position. See Henk's lecture 2: http://www1.mpi-halle.mpg.de/~henk/
 
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  • #3

FAQ: [Q] Time uncertainty and particle energy similar to photon

What is time uncertainty?

Time uncertainty is a concept in physics that refers to the inherent uncertainty in measuring the time of an event. This is due to the fact that time is not an absolute quantity and can be affected by factors such as the observer's frame of reference and the speed of the particles involved.

How is particle energy similar to a photon?

Particle energy and photon energy are both forms of energy that are associated with particles. In the case of photons, the energy is related to the electromagnetic radiation they carry. In the case of particles, the energy is related to their mass and velocity.

What is the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This also applies to time and energy, meaning that the more accurately we measure one, the less accurately we can measure the other.

How does time uncertainty affect particle energy?

Time uncertainty can affect particle energy in a few ways. Firstly, it means that the exact energy of a particle cannot be known with absolute certainty. Additionally, due to the uncertainty in time measurements, there may be slight variations in the energy of a particle over time.

Can particles have different energy levels due to time uncertainty?

Yes, particles can have different energy levels due to time uncertainty. This is because the uncertainty in time measurements can lead to slight variations in the energy of a particle. This is especially significant for particles with very short lifetimes, such as those involved in nuclear reactions.

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