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I think I've solved the equations of motion for a particle in this one-dimensional potential -

V(x) = -k/(a-x) - k/(a+x) with |x| < a, a is real +ve, x is real.

K is a constant of suitable dimension.

It's a charge between two like charges with separation 2*a.

I start with the force equation

m*x'' = -4*a*k*x / (a^2 - x^2)^2

(Using ' to indicate differentiation wrt time)

I can integrate this to get

m*x' = sqrt(2*k*a)/sqrt(a^2 - x^2)

This ought to be textbook example, can anyone point me to an authoritative solution or come up with x ?

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# Interesting oscillator potential

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