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Power Series expansion of an eigenvalue

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  1. Feb 7, 2017 #1
    1. ... Expand the Eigenvalue as a power series in epsilon, up to second order:
    λ=[3+√(1+4 ε^2)]V0 / 2

    2. Relevant equations
    I am familiar with power series, but I don't know how to expand this as one.



    3. The attempt at a solution: I have played around with the idea of using known power series of functions such as e^x, yet I haven't found a way to make that useful.
     
    Last edited: Feb 7, 2017
  2. jcsd
  3. Feb 7, 2017 #2

    BvU

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    Dunno is not good enough according to PF guidelines
    But do I detect a term ##\sqrt{1+4\varepsilon^2}## in there ?
     
  4. Feb 7, 2017 #3
    Please review my post again. Hopefully it is both more legible and up to PF guidelines.
     
  5. Feb 8, 2017 #4

    BvU

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    I still detect a term ##
    \sqrt{1+4\varepsilon^2\;}## ! How would you develop that into a power series in ##\varepsilon##, up to second order ?

    And the guidelines tell you 'Dunno' ('Don't know') isn't good enough...
     
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