Eigenfunctions, eigenstates and eigenvalues

  • Thread starter Harper
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  • #1
Harper
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Homework Statement


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,......?




Homework Equations




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.
 

Answers and Replies

  • #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}}## ??
 
  • #3
Harper
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Yes you read it correctly and no I didn't write that out.
 
  • #5
Harper
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Hey thanks for the tool and I think I have it figured out. Thank you for the help.
 
  • #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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