Components for the angular momentum operator L

[QMquestions]

Homework Statement

Consider wavefunction psi (subscript "nlm") describing the electron in the stationary state for the hydrogen atom with quantum numbers n,l,m and the third component L3 for the orbital angular momentum operator L. What is the expectation value of L3 and of L3^2 for the state described by psi?

Homework Equations

The Attempt at a Solution

L = sqrt(l(l+1)*hbar).

And I think L3 is the same as Lz
Lz = m*hbar
but I don't know what stationary state implies in terms of quantum numbers.

 

[QMquestions]

To add to my attempt at a solution:

<L3> = <Lz> = integral(-inf to inf of(psi* x L3operator x psi dz)

L3 operator = (-i x hbar) x (partial / partial x phi)

 

[malawi_glenn]

stationary means that it does not depend on time, no time dependence.

 

[QMquestions]

does that have implications on the orbital angular momentum operator?

 

[malawi_glenn]

no, hint: write the solutions in terms of spherical harmonics and use the property of L_z operator on those.