The quantization of the Hamiltonian in curved space

The construction of the quantum-mechanical Hamiltonian by canonical quantization is examined. The results are used to enlighten examples taken from slow nuclear collective motion. Hamiltonians, obtained by a thoroughly quantal method (generator-coordinate method) and by the canonical quantization of the semiclassical Hamiltonian, are compared. The resulting simplicity in the physics of a system constrained to lie in a curved space by the introduction of local Riemannian coordinates is emphasized. In conclusion, a parallel is established between the result for various coordinates and a proposed procedure for quantizing the semiclassical Hamiltonian for a single coordinate.Partially supported by Fundação Calouste Gulbenkian, Lisboa.