Does this operator commute with the Hamiltonian operator?

tarkin
Messages
13
Reaction score
0

Homework Statement


Show that the mean value of a time-independent operator over an
energy eigenstate is constant in time.

Homework Equations


Ehrenfest theorem

The Attempt at a Solution


I get most of it, I'm just wondering how to say/show that this operator will commute with the Hamiltonian operator.
Is it correct to say that because they both act on energy eigenstates, they must commute?
If so, is there a way to show this?
 
Physics news on Phys.org
What is the form of the time-dependent energy eigenfunction? Say at ##t=0## this eigenfunction is ##|n\rangle## having energy ##E_n##, how does it look like at a later time ##t##?
 
Thread 'Need help understanding this figure on energy levels'

Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
View full post »
Thread 'Understanding how to "tack on" the time wiggle factor'

Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
View full post »

Similar threads

Operator that commutes with the Hamiltonian
Replies
3
Views
2K
Angular momentum operator for 2-D harmonic oscillator
Replies
2
Views
3K
Unitary vector commuting with Hamiltonian and effect on system
Replies
8
Views
2K
Time Inversion Symmetry and Angular Momentum
Replies
1
Views
2K
Commutator of the Dirac Hamiltonian and gamma 5
Replies
2
Views
3K
Commutate my hamiltonian H with a fermionic anihillation operator
Replies
3
Views
2K
Is <E> for an Electron in a Coulomb Field Time-Dependent?
Replies
5
Views
3K
A Hamiltonian commutes with a parity operator -- What does that mean?
Replies
7
Views
3K
Momentum Eigenstate with a non-zero potential
Replies
1
Views
2K
I Significance of the Exchange Operator commuting with the Hamiltonian
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top