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We construct a closed system of equations describing the quark--anti-quarkpotential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It isbased on the Quantum Spectral Curve method supplemented with a novel type ofasymptotics. We present a high precision numerical solution reproducing theclassical and one-loop string predictions very accurately. We also analyticallycompute the first 7 nontrivial orders of the weak coupling expansion.  Moreover, we study analytically the generalized quark--anti-quark potentialin the limit of large imaginary twist to all orders in perturbation theory. Wedemonstrate how the QSC reduces in this case to a one-dimensional Schrodingerequation. In the process we establish a link between the Q-functions and thesolution of the Bethe-Salpeter equation.

Quark--anti-quark potential in N=4 SYM