Group Abstract Group Abstract

Message Boards Message Boards

0
|
6.5K Views
|
4 Replies
|
0 Total Likes
View groups...
Share
Share this post:

Fitting a periodic potential?

Posted 10 years ago

I will use this potential to calculate some physical properties

enter image description here

to do so, I need to find a fitting function. The series expansion

a0+Cos[x] a1+Cos[x]^2 a2+Cos[x]^3 a3+Cos[x]^4 a4+Cos[x]^5 a5+b0+Sin[x] b1+Sin[x]^2 b2+Sin[x]^3 b3+Sin[x]^4 b4+Sin[x]^5 b5

truncated at the 5th degree gives the following fitting

enter image description here

Which could serve the purpose except that periodicity disappears at the beginning of the curve: the well becomes deeper than what it should be. How can I enforce periodicity on the fitting function?

POSTED BY: Eft Rsd
4 Replies

In case you do not need an analytic expression, then

Interpolation[(* your data *), PeriodicInterpolation -> True]

might be helpful.

POSTED BY: Henrik Schachner
Posted 10 years ago

Interpolation works fantastically but I need the fitting function itself because I need to calculate Hamiltonian matrix elements. After using Interpolation it is possible to perform integration and differentiation on the InterpolatingFunction, but it is not possible to do that when combining the InterpolatingFunction with other expressions.

POSTED BY: Eft Rsd

As an alternative to a Fourier expansion, the curve you have drawn can be well represented by 6 connected linear segments, repeated periodically.

POSTED BY: S M Blinder
Posted 10 years ago

I actually need to use the Fourier series because I will repeat the process on much smoother potentials. I have tried Fourier series to fit another more wiggling potential and the same problem occurred; the first well became deeper.

POSTED BY: Eft Rsd
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard