1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Selection rules electrostatic field

  1. Mar 8, 2012 #1
    Hi all , I need some help with this problem,
    1. The problem statement, all variables and given/known data

    A hydrogen atom, which is in its ground state |1 0 0 > , is put into a weak time-dependent external electric field, which points into the z direction:
    [tex]\boldsymbol{E}(t,\boldsymbol{r}) = \frac{C\hat{\text{e}}_{z}}{t^{2}+\tau ^{2}}[/tex], where C and [tex]\tau > 0[/tex] and e are constants. This gives rise to a perturbation potential [tex]V(t) = C\frac{e\hat{z}}{t^{2}+\tau^{2}}[/tex].
    Using lowest-order time-dependent perturbation theory, find the selection rules for transitions from the ground state, i.e. find out which final state values for the quantum numbers n, l and m are possible in transitions from the ground state.


    2. Relevant equations

    [tex]P_{fi}(t,t_{0})\equiv |\langle\phi_{f}|\psi(t)\rangle|^{2}\approx \frac{1}{\hbar^{2}}\left|\int_{t_{0}}^{t}\text{d}t _{1}\langle\phi_{f}|V_{S}(t_{1})|\phi_{i}\rangle \text{e}^{\text{i}(E_{f}-E_{i})t_{1}/\hbar}\right|^{2}.[/tex]

    3. The attempt at a solution

    First, I have to see the values of m for which the sandwich vanish i.e. [tex]< n l m| \hat{z} | 1 0 0 > =0 [/tex]

    [tex]< n l m| \hat{z} | 1 0 0 > = I (radial ) χ \int Y^*_{l,m} Cos [\theta]d \Omega Y_{0,0} [/tex]

    The radial part is always non zero,

    Therefore , i have to compute
    [tex]\int d \Omega Y^*_{l,m} \cos (\theta) Y_{0,0} = [/tex] But I don't know what I can use, to compute the terms \cos (\theta) X spherical harmonics
    thanks for your help!
     
  2. jcsd
  3. Mar 9, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Hint: Look up Y1,0.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Selection rules electrostatic field
  1. Selection rule (Replies: 3)

Loading...