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Here's an interesting function:

x^4 - 2(x^2) + 1

It has a local maximum at (0,1) and two local minima at (-1,0) and (1,0). The shape in between is a smooth bell shape.

Could be useful for interpolation purposes.
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If you take the parameter as a complex valued scalar field, thats a form of the 'mexican hat' potential! HOORAY!

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