A natural normalization for the eigenstates of a Hamiltonian with continuous spectrum

A mathematical formalism that allows to deal with many problems on quantum systems with continuous evolution spectrum is presented. The usual Hilbert space is generalized to a prehilbert one T where singular states can be represented and an extended Dirac's notation can be introduced. The obtained formalism contains the Van Hove one but in a more natural way. It allows to explain decoherence and other phenomena.