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I Does measurement change the energy of a system?

  1. Jun 18, 2017 #1
    Suppose, the energy of a particle is measured, say ##E_1##. So now the state vector of the particle is the energy eigenket ##|E_1>##.
    Then the position of the particle is measured, say ##x##. As the Hamiltonian operator and the position operator are non-commutative, the state vector is changed to the position eigenket ##|x>## which is different from ##|E_1>##.
    Now the energy is measured again. As the state vector is no longer ##|E_1>##, it is not guaranteed that the energy is still ##E_1## as the first measurement.
    Does the measurement change the amount of energy of the system? How doesn't this violate the law of energy conservation?
     
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  3. Jun 18, 2017 #2

    Vanadium 50

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    Even classically this happens. If you pick up an object and put it on a table to measure it with a ruler, haven't you changed its energy?
     
  4. Jun 18, 2017 #3

    hilbert2

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    You can make the kinetic energy expectation value of a free particle arbitrarily large by just measuring its position accurately enough. This is because a perfectly localized particle can have any momentum with equal probability. There's no way to measure a position without interacting with the particle, and the more precise you want to make the measurement, the higher energy scattering processes are required.
     
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