Do the observables for d/dx and x^2 commute?

  • Thread starter Thread starter user14
  • Start date Start date
  • Tags Tags
    observables
user14
Messages
1
Reaction score
0

Homework Statement


Are the observables corresponding to the d/dx and x^2 operators complementary?


Homework Equations


none


The Attempt at a Solution


I know that if the operators do not commute then their corresponding observables are complementary. I just don't know how to show mathematically that they don't commute.
 
Physics news on Phys.org
Use the commutator definition [A,B]=AB-BA to show if they commute or not.
 
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
Does this operator commute with the Hamiltonian operator?
Replies
1
Views
2K
Commutation and Measurement of Observables
Replies
4
Views
2K
Quantum Virial Theorem Derivation
Replies
10
Views
2K
Proving the Commutation Relation for Quantized Boson in a One-Dimensional Box
Replies
1
Views
1K
Massless theories can be conformally invariant
Replies
1
Views
2K
Constants of motion in quantum mechanics
Replies
1
Views
2K
Spacetime and Geometry: Vanishing commutators#2
Replies
4
Views
2K
Spacetime and Geometry: Vanishing commutators
Replies
1
Views
2K
Momentum Eigenstate with a non-zero potential
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top