Do eigenstate probabilities change with time?

[sgphysics]

To my understanding any quantum system can be describes as a linear combination of eigenstates or eigevectors of any hermetian operator, and that the eigen values represent the observable properties. But how does the system change with time? I suppose big systems with many particles change with time. Do the weights for the different eigenstates change with time?

 

[anuttarasammyak]

We have time dependent Shrodinger equation to describe time evolution of the states. For an example in diffusion of Gaussian wave function in free space, weights of different position eigenstates change with time.

 

[PeroK]

To my understanding any quantum system can be describes as a linear combination of eigenstates or eigevectors of any hermetian operator, and that the eigen values represent the observable properties. But how does the system change with time? I suppose big systems with many particles change with time. Do the weights for the different eigenstates change with time?

An energy eigenstate is also called a stationary state because the expectation value of all observables is independent of time. This is not the case for a superposition of energy eigenstates.

The expectation value of any observable whose operator commutes with the Hamiltonian does not change over time. For other observables the expectation value may be time dependent, as above.

E.g. if you have the quantum harmonic oscillator in a superposition of energy eigenstates, then the expectation values of position and momentum change harmonically over time.

PS this assumes a time independent Hamiltonian. If the Hamiltonian itself depends on time then in general so do all observables.