  We analyze the cusp anomalous dimension in the (leading) ladder limit of
$\mathcal N=4$ SYM and present new results for its higher-order perturbative
expansion. We study two different limits with respect to the cusp angle $\phi$.
The first is the light-like regime where $x = e^{i\,\phi}\to 0$. This limit is
characterised by a non-trivial expansion of the cusp anomaly as a sum of powers
of $\log x$, where the maximum exponent increases with the loop order. The
coefficients of this expansion have remarkable transcendentality features and
can be expressed by products of single zeta values. We show that the whole
logarithmic expansion is fully captured by a solvable Woods-Saxon like
one-dimensional potential. From the exact solution, we extract generating
functions for the cusp anomaly as well as for the various specific
transcendental structures appearing therein. The second limit that we discuss
is the regime of small cusp angle. In this somewhat simpler case, we show how
to organise the quantum mechanical perturbation theory in a novel efficient way
by means of a suitable all-order Ansatz for the ground state of the associated
Schr\"odinger problem. Our perturbative setup allows to systematically derive
higher-order perturbative corrections in powers of the cusp angle as explicit
non-perturbative functions of the effective coupling. This series approximation
is compared with the numerical solution of the Schr\"odinger equation to show
that we can achieve very good accuracy over the whole range of coupling and
cusp angle. Our results have been obtained by relatively simple techniques.
Nevertheless, they provide several non-trivial tests useful to check the
application of Quantum Spectral Curve methods to the ladder approximation at
non zero $\phi$, in the two limits we studied.
