  The similarity between classical and quantum physics is large enough to make
an investigation of quantization methods a worthwhile endeavour. As history has
shown, Dirac's canonical quantization method works reasonably well in the case
of conventional quantum mechanics over $\mathbb{R}^n$ but it may fail in
non-trivial phase spaces and also suffer from ordering problems. Affine
quantization is an alternative method, similar to the canonical quantization,
that may offer a positive result in situations for which canonical quantization
fails. In this paper we revisit the affine quantization method on the half
line. We formulate and solve some simple models, the free particle and the
harmonic oscillator.
