# Effects of measurement on particle energy

According to quantum mechanics, once you measure a particle's energy, its wave function collapse into some state, an eigenfunction with some eigenvalue (which is the particle energy). But if a particle is at some stationary state, the Schrödinger equation tells us the wave function at any time t, will be the same eigenfunction multiplied by some phase. From this, we can derive the particle will have constant energy. But it means, if I take a particle with some complex wave function and measure its energy at some time, I made his energy constant ? How does it make sense ?

• If you prepare a state in an eigenstate of the energy operator, then it won't change over time. If you measure the energy of an arbitrary state then the state will collapse to an energy eigenstate. I can't see any contradiction here. – user183962 May 21 at 8:10
• So if you take some particle which is affected by some forces and has a very complex wave function, by measuring it, did you make its energy constant from now on? Real objects don't remain invariant in time, That is sort of my question. I know there isn't a contradiction here, but I still can't understand why it makes sense. – Michael May 21 at 8:31
• Wave function complexity doesn't have any importance. When you measure the energy it collapse to an eigenstate and if the energy operator is the same for the system then there will be only a phase as you mentioned. – user183962 May 21 at 8:35
• I think part of the confusion is that you're thinking the system is not isolated. If there are external forces etc, then the Hamiltonian will be time dependent and energy eigenstates won't be stationary. – jacob1729 May 21 at 9:50
• You are narrating a straightforward sequence of facts and are then asking as to why they make sense. I feel clueless as to how to answer if I don't know as to why you think they shouldn't make sense. – Dvij Mankad May 21 at 12:52