Consider the below functional
$F=\int_0^L dx [d_x f(x)]^2,$
with boundary conditions
$\cos 2 f(0)=\cos 2 f(L),$
$\sin 2 f(0)=\sin 2 f(L)$.
The set of functions $f(x)=\frac{n \pi x}{L}$ (with integer $n$), are local minimums of $F$. Is it possible to find the height of the barrier between two local minimums say between n= n1 and n=n1+1?
As an example, in the below figure, the barrier height is $\Delta F$. However, in this graph a function is plotted instead of a functional.
