Schroedinger equation with angular momentum operators

[damien88]

Hi, I have just started looking at angular momentum in quantum mechanics and I am considering the question, ''Write down the Schrödinger-like equations for the orbital angular momentum operators L^2 and Lz. Would I be correct in thinking this would be;

L^2|ψ=l(l+1)ħ|ψ
Lz|ψ=mlħ|ψ


Thanks in advance

 

[jfy4]

If I understand your question, you are close. Take a look at the units of the first equation, the left and right sides don't match.

 

[Matterwave]

Those are Eigenvalue equations, and are true if your wavefunction are eigenfunctions of the respective operators with those eigenvalues. They are not true for general wavefunctions.

I also wouldn't call them Schroedinger-like, since they do not tell you the time evolution of the wave-function. I don't really know what you are looking for though.

 

[damien88]

The question itself has been lifted straight from a text and that's what is causing me some issues as I don't fully undertsand exactly what it is looking for.I believe it is just the general waveform I am looking for in this instance.

edit:

Ok, so now I have

E|ψ(t)=L^2/2I||ψ(t)

but I ma still unsure as to how this equation would look using Lz as the operator.