Orthogonal Functions: Questioning the Reason Why

Logarythmic
Messages
277
Reaction score
0
A question for my understanding:

If I have an operator \cal{L} and a set of eigenfunctions \phi_n of this operator, then the eigenfunctions are orthogonal. Why is that?
 
Physics news on Phys.org
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

Quantum Mechanics hydrogen atom eigenfunction problem
Replies
1
Views
2K
Quantum Mechanics homework question on wavefunctions
Replies
4
Views
2K
Instantaneous doubling of the Infinite Square Well Width
Replies
1
Views
4K
Does operator L^2 commute with spherical harmonics?
Replies
2
Views
2K
I Validity of identical eigenfunction of commutating operators
Replies
12
Views
216
Perturbation Theory: Finding Eigenfunctions and Energies
Replies
2
Views
2K
Why are fermion states anti-symmetric under exchange operator?
Replies
1
Views
1K
I The last step of this Green's function proof is not clear
Replies
7
Views
830
If A and B are Hermitian operators is (i A + B ) Hermitian?
Replies
4
Views
4K
I QM Orthogonality: Separate & Independent Eigenvalues?
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top