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[Q] Time uncertainty and particle energy similar to photon

  1. Nov 6, 2008 #1
    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 enery 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] ?
     
  2. jcsd
  3. Nov 6, 2008 #2

    atyy

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    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/
     
  4. Nov 6, 2008 #3

    atyy

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