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 ?  
 A: The simple picture is that quantum mechanical differential equations have to be solved in order to have quantum mechanical wavefunctions, and boundary conditions have to be imposed so as to pick for the particular potential the particular wavefunction describing the system.
Take the hydrogen atom at its ground state : that is one solution of the Schrodinger equation, and it will stay there forever, if no new boundary conditions/interactions are imposed. A photon hitting the hydrogen atom with the ionization energy will be a different solution of the differential equation, and the wave function will no longer be of the ground state but of the free ion.That is the meaning of "collapse", a change in the wavefunction due to an interaction.
With many body problems one uses quantum field theory based on plane wave solutions of the differential equations, but the logic is the same: the boundary conditions have to be taken into account for the solution and any change in the boundary conditions, changes the wavefunction, which is what "collapse" is about. So a system in an energy eigenstate will stay there until there is an interaction, i.e. a change in the boundary conditions of the problem, which a scattering, for example , will induce. Then a different wavefunction will describe the system.

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.

The energy  is constant only for this point measurement in time, i.e you have the information that it was in  that measured energy eigenstate. In the hydrogen example above,  the kicked out electron signals that the atom + electron are now in a different solution of the problem at hand, a different wavefunction, where the proton is alone and the electron just outside it, with zero momentum , a different wavefunction; and then it is ready to fall back into the original mathematically  wave function by emitting a photon,by  a  new interaction.
Collapse means "change of wavefunction describing the system".
