Does measurement change the energy of a system?

[arpon]

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?

 

[Vanadium 50]

Does the measurement change the amount of energy of the system? How doesn't this violate the law of energy conservation?

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?

 

[hilbert2]

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?

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.