Components for the angular momentum operator L


by QMquestions
Tags: angular, momentum, operator, orbital, stationary state
QMquestions
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#1
Mar4-09, 11:36 PM
P: 3
1. The problem statement, all variables and given/known data

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?


2. Relevant equations



3. 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.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
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QMquestions
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#2
Mar5-09, 12:23 AM
P: 3
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
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#3
Mar5-09, 02:10 AM
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stationary means that it does not depend on time, no time dependence.

QMquestions
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#4
Mar5-09, 04:08 AM
P: 3

Components for the angular momentum operator L


does that have implications on the orbital angular momentum operator?
malawi_glenn
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#5
Mar5-09, 04:12 AM
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no, hint: write the solutions in terms of spherical harmonics and use the property of L_z operator on those.


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