[Q] Time uncertainty and particle energy similar to photon

[good_phy]

Hi i applied $i\hbar \frac{\partial}{\partial x}$ to energy eigen state which is

evolving in time, $e^{(i(kx-wt)}$ and i get energy eigen value $\hbar w <br />$

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 $[i\hbar \frac{\partial}{\partial x},t] = \hbar^2$ and corresponding uncertainty $\Delta E \Delta t \geq \frac{\hbar}{2}$

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 $e^{(i(kx-wt)}$ ?

 

[atyy]

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/

 

[atyy]

There is no time-energy uncertainty principle:
Nikolic, Quantum mechanics: Myths and facts
http://arxiv.org/abs/quant-ph/0609163