  At small lattice spacing, or when using e.g. overlap fermions, lattice QCD
simulations tend to become stuck in a single topological sector. Physical
observables then differ from their full QCD counterparts by 1/V corrections,
where V is the spacetime volume. Brower et al. and Aoki et al. have derived
equations by means of a saddle point approximation, to determine and to remove
these corrections. We extend these equations and apply them to a simple toy
model, a quantum mechanical particle on a circle in a square well potential at
fixed topology. This model can be solved numerically up to arbitrary precision
and allows to explore effects arising due to fixed topology. We investigate the
range of validity and accuracy of the above mentioned equations, to remove such
fixed topology effects.
