  A quantum navigation problem concerns the identification of a time-optimal
Hamiltonian that realises a required quantum process or task, under the
influence of a prevailing `background' Hamiltonian that cannot be manipulated.
When the task is to transform one quantum state into another, finding the
solution in closed form to the problem is nontrivial even in the case of
time-independent Hamiltonians. An elementary solution, based on trigonometric
analysis, is found here when the Hilbert space dimension is two. Difficulties
arising from generalisations to higher-dimensional systems are discussed.
