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Homework Help: Expansion of the wave equation for a stationary wave

  1. Nov 10, 2018 #1
    1. The problem statement, all variables and given/known data
    A generic state represented by the wave function ##\psi (\vec(x)## can be expanded in the eigenstates with defined angular momentum. Write such an expansion for a plane wave travelling along the z direction with momentum ##p = \hbar k## in terms of unknown coefficients ##c ( k ′ )_ {l m}## . Show that ##c ( k )_{ l m} are non-zero only if k' = k and m = 0

    2. Relevant equations


    3. The attempt at a solution

    I don't know where to start. I could of course go the long way, introducing dimensionless variables, do a power series ansatz and solve de DE with frobinious trick. But it seems the answer will be way easier than that if you just know how to approach it.
     
    Last edited by a moderator: Nov 10, 2018
  2. jcsd
  3. Nov 11, 2018 #2
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