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I am new to python and wish to calculate a wavefunction by fitting 1D data to a linear combination of spherical harmonics.

I am thinking of expressing wavefcntion as follows

wavefcuntion = aY0+bY1+c*Y2......Yn

and then fit cofficient using curve fitting fucntion in scipy.optimize

The method I tried is explained below

I am doing as follows:

y0= scipy.special.sph_harm(0,0,0,0) y1=scipy.special.sph_harm(1,2,-1,1) y2= ......

and so on.

def wavefun(a,b,c): ##a,b,c are expansion coefficients return ay0+by1+c*y2

newwave=scipy.optimize.curvefit(wavefun, x, y) ##assume I have x, y data

this approach is working, but I will have hundreds of spherical harmonics and expansion coefficients for real work. how do I make this process more efficient?

Keshav Kumar Singh
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  • I'd also suggest further explaining the math side of this in a math.stackexchange.com post to get more eyes on it. It's likely that the biggest performance improvement would come from finding good mathematical methods, not the programming part. – Kaia Feb 24 '23 at 18:46

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