Why is the energy expectation value independent of time?

[cragar]

It seems that the energy expectation value is independent of time.
I did it for an infinite square well. And when you time evolve your wave function
the time evolution cancels when you complex conjugate it and then do the integral.
<E>=<ψ|E|ψ> it seem like this might always independent of time, What do you guys think.
I guess I could try to prove it in general.

 

[Jazzdude]

It seems that the energy expectation value is independent of time.

That's called energy conservation and should not be so surprising. It's true as long as the hamiltonian is time independent. And it generalized to the expectation value of any operator that commutes with the hamiltonian.

 

[mfb]

If you have a time-independent Hamiltonian, energy is always conserved in your system. This is a very fundamental result and it works both in classical and quantum mechanics.

 

[cattlecattle]

It seems that the energy expectation value is independent of time.
I did it for an infinite square well. And when you time evolve your wave function
the time evolution cancels when you complex conjugate it and then do the integral.
<E>=<ψ|E|ψ> it seem like this might always independent of time, What do you guys think.
I guess I could try to prove it in general.

A more general result is the Ehrenfest theorem: http://en.wikipedia.org/wiki/Ehrenfest_theorem