B Do eigenstate probabilities change with time?

sgphysics
Messages
20
Reaction score
2
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?
 
Physics news on Phys.org
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.
 
Last edited:
sgphysics said:
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.
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
Back
Top