I don't know how that could be done.

I can approximate a simple harmonic oscillator as follows:

In[25]:= AbsoluteTiming[sho = cmpt[10000 (x - 1/2)^2, 5, 1/1000];]

During evaluation of In[25]:= {{Solve_Succeeded,1}}

During evaluation of In[25]:= {{Solve_Succeeded,1}}

During evaluation of In[25]:= {{Solve_Succeeded,1}}

During evaluation of In[25]:= {{Solve_Succeeded,1}}

During evaluation of In[25]:= {{Solve_Succeeded,1}}

Out[25]= {7.70231, Null}

 energy levels

In[26]:= sho[[1]]

Out[26]= {99.9994, 299.997, 499.992, 699.985, 899.977}

 test spacing

In[27]:= Table[sho[[1, n]]/(n - 1/2), {n, 5}]

Out[27]= {199.999, 199.998, 199.997, 199.996, 199.995}

In[28]:= Table[ListPlot[Table[{x, psi[x]}, {x, 0, 1, 1/100}] /. sho[[2, n]], 
  Joined -> True], {n, 5}]

Hello Frank,

I don't know what has happened earlier, but in the meantime I could download and open the notebook. Alas, to no avail, because I have only Mathematica 7 and no access to ParametricIPOPTMinimize.

Beste Grüße Hans

I didn't try collocation because I felt it would be easier to do optimization with a complicated objective function and a small number of constraints, as opposed to solving a lot of coupled equations from collocation. .

Dr. Frank: Neat application of IPOPT! Just curious how the optimization approach compares to solution via collocation method. I surmise the collocation might not (gracefully) handle the eigenfunction orthogonality constraint?