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Eigenfunctions, eigenstates and eigenvalues

  1. Oct 12, 2016 #1
    1. The problem statement, all variables and given/known data
    The problem states consider A_hat=exp(b*(d/dx)). Then says ψ(x) is an eigenstate of A_hat with eigenvalue λ, then what kind of x dependence does the function ψ(x) have as x increases by b,2b,......?




    2. Relevant equations


    3. The attempt at a solution
    Started out by doing (A_hat)ψ(x+b), turned that into (A_hat)ψ(x)+(A_hat)ψ(b). Not sure where to go from there and/or how to incorporate λ.
     
  2. jcsd
  3. Oct 12, 2016 #2

    Simon Bridge

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    Did you write out the eigenvalue equation?
    Note: you are asked what happens with ##\psi(x)\to\psi(x+nb): n=1,2,3,\cdots##
    ie - how does ##\psi## depend on ##x##?

    Do I read this correctly: ##\hat A = e^{b\frac{d}{dx}}## ??
     
  4. Oct 12, 2016 #3
    Yes you read it correctly and no I didn't write that out.
     
  5. Oct 12, 2016 #4

    Simon Bridge

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  6. Oct 13, 2016 #5
    Hey thanks for the tool and I think I have it figured out. Thank you for the help.
     
  7. Oct 13, 2016 #6

    Simon Bridge

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    Well done - what did you figure out (just for other people stuck on the same thing...)?
     
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