  We describe generally deformed Heisenberg algebras in one dimension. The
condition for a generalized Leibniz rule is obtained and solved. We analyze
conditions under which deformed quantum-mechanical problems have a Fock-space
representation. One solution of these conditions leads to a q-deformed
oscillator already studied by Lorek et al., and reduces to the harmonic
oscillator only in the infinite-momentum frame. The other solution leads to the
Calogero model in ordinary quantum mechanics, but reduces to the harmonic
oscillator in the absence of deformation.
