# Power Series expansion of an eigenvalue

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1. Feb 7, 2017

### ExplosivePete

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. Feb 7, 2017

### BvU

Dunno is not good enough according to PF guidelines
But do I detect a term $\sqrt{1+4\varepsilon^2}$ in there ?

3. Feb 7, 2017

### ExplosivePete

Please review my post again. Hopefully it is both more legible and up to PF guidelines.

4. Feb 8, 2017

### BvU

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...