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Energy of a state of a hydrogenic atom

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data
    One of a He+ atom is in a pure state |1,0,0>. What is the energy of this state? Give a numerical answer in eV. Another of these is found to be in a mixed state: |si>=[1/(3^1/2)][2^1/2|2,1,0>+|2,1,-1>. Calculate the following expectation values at t=0; <E>,<Lz>,<Lx> HINT: start by writing Lx in terms of the raising and lowering operators, L+ and L-


    2. Relevant equations
    ???


    3. The attempt at a solution
    I think I'm supposed to calculate the ground state? I'm not sure what formula to use.
     
    Last edited: Feb 23, 2010
  2. jcsd
  3. Feb 23, 2010 #2
    The He+ ion behaves like a hydrogen atom with double-charged nucleus (Z=2). Hence the corresponding expression for hydrogen energy levels can be used.

    Relevant equations:

    [tex]
    E_{|n,l,m>} = -\frac{m_e Z^2 e^4}{2\hbar^2} \frac{1}{n^2}
    [/tex]

    [tex]
    \hat{L}_\pm = \hat{L}_x \pm i\hat{L}_y
    [/tex]
     
  4. Feb 23, 2010 #3
    Ok, so I found the energy, <E>, and <Lz>, but how do I determine <Lx>? I tried writing it in terms of L+-, but I ended up just proving the equation true or having to deal with Ly. I need to know what Lx|n,l,m> is, but I can't figure it out!
     
    Last edited: Feb 23, 2010
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