  Triviality and Landau poles are often greeted as harbingers of new physics at
1 TeV. After briefly reviewing the ideas behind this, a model of singular
quantum mechanics is introduced. Its ultraviolet structure, as well as some
features of its vacuum, related to triviality, very much parallel
$\lambda\phi^4$. The model is solvable, exactly and perturbatively, in any
dimension. From its analysis we learn that Landau poles do not appear in any
exactly computed observable, but only in truncated perturbation theory, when
perturbation theory is performed with the wrong sign coupling. If these
findings apply to the standard model no new physics at 1 TeV should be expected
but only challenges for theorists.
