Components for the angular momentum operator L

  1. 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
     
  2. jcsd
  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)
     
  4. malawi_glenn

    malawi_glenn 4,726
    Science Advisor
    Homework Helper

    stationary means that it does not depend on time, no time dependence.
     
  5. does that have implications on the orbital angular momentum operator?
     
  6. malawi_glenn

    malawi_glenn 4,726
    Science Advisor
    Homework Helper

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