Quantizing preserving Noether symmetries

A procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed. This new quantization scheme preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schroedinger equation. Two examples are given, one known and one new: the quantization of a charged particle in a uniform magnetic field in the plane, and that of the ‘goldfish’ many-body problem extensively studied by Calogero et al.