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Stark Effect

  1. Apr 13, 2014 #1
    In order to apply perturbation theory to the ψ[itex]_{200}[/itex] and ψ[itex]_{210}[/itex] states, we have to solve the matrix eigenvalue equation.

    Ux=λx where U is the matrix of the matrix elements of H[itex]_{1}[/itex]= eEz between these states.

    Please see the matrix in attachment 1.

    where <2,0,0|z|2,1,0>=<2,1,0|z|2,0,0>=3a[itex]_{o}[/itex]

    Solving this matrix we get, λ[itex]_{1}[/itex]=3ea[itex]_{o}[/itex]|E| and λ[itex]_{2}[/itex]= -3ea[itex]_{o}[/itex]|E|

    Then we find eigenvectors to get x[itex]_{1}[/itex] =(1/√2 1/√2)[itex]^{T}[/itex] and x[itex]_{2}[/itex]= (1/√2 -1/√2)[itex]^{T}[/itex]

    **** They finally said that ψ[itex]_{1}[/itex] = (ψ[itex]_{200}[/itex] + ψ[itex]_{210}[/itex])/√2

    and ψ[itex]_{2}[/itex] = (ψ[itex]_{200}[/itex] - ψ[itex]_{210}[/itex])/√2

    How did they get this? How did they combine ψ[itex]_{1}[/itex] and ψ[itex]_{2}[/itex] as follows? It is just the linear combination that I don't get. Thank you.

    Attached Files:

    Last edited: Apr 13, 2014
  2. jcsd
  3. Apr 13, 2014 #2
    Please note that this is for Hydrogen atom, n=2 where we have degeneracy!
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