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I have a scenario where in trying to solve for the ground-state of a Hamiltonian, I require to be able to solve some coupled differential equations.

Prior to this I have already set k=1 and Δ=5

$$ \text{NDSolve}\left[\left\{\Delta \delta (\phi )-i k e^{-i \phi } \beta (\phi )==-i \alpha '(\phi ),\beta (\phi )-\Delta \gamma (\phi )+i k e^{i \phi } \alpha (\phi )==i \beta '(\phi ),-\Delta \beta (\phi )+i k e^{i \phi } \delta (\phi )==-i \gamma '(\phi ),\Delta \alpha (\phi )+\delta (\phi )-i k e^{-i \phi } \gamma (\phi )==i \delta '(\phi ),\alpha (\pi )==1,\beta (\pi )==-1,\gamma (\pi )==1,\delta (\pi )==-1\right\},\{\alpha ,\beta ,\gamma ,\delta \},\{\phi ,-\pi ,\pi \}\right] $$

Source Code:

NDSolve[{- E^(-I ϕ) β[ϕ] I k + Δ δ[ϕ] == -I α'[ϕ] ,
  (E^(I ϕ)) α[ϕ] I k  + β[ϕ] - Δ γ[ϕ] ==  I β'[ϕ],
  - Δ β[ϕ] +E^(I ϕ) δ[ϕ] I k == -I γ'[ϕ],
  Δ α[ϕ]-E^(-I ϕ) γ[ϕ] I k +δ[ϕ] ==I δ'[ϕ],
  α[π]==1, β[π]==-1, γ[π]==1, δ[π]== -1},{α,β,γ,δ},{ϕ,-π,π}]

It gives me an error of

NDSolve::ndode: Input is not an ordinary differential equation.

Here's a screen shot of the error on my system: i.stack.imgur.com/14Dwr.png

Any idea what i'm doing wrong?

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would you happen to have the source code for this by any chance? will be easier. –  Nasser Jun 18 '14 at 12:30
I was trying to enter it, but it came up as [\Alpha] etc. how do i change that? –  user16010 Jun 18 '14 at 12:36
put all the source code in one cell. Then do cell->convert to->input form, then select the cell and right-click and do COPY AS->Plain text, then paste it here. –  Nasser Jun 18 '14 at 12:46
You did not copy the whole cell. Code is missing. !Mathematica graphics also I see [Pi] Did you mean to do this? –  Nasser Jun 18 '14 at 13:15
@Nasser: Sorry. I had copied it properly, but the formatting had pushed the last few characters out of the code block. Edited and corrected. –  user16010 Jun 18 '14 at 13:24

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