Method for the construction of the Lewis-Riesenfeld time-dependent invariants and their eigenvalue equations

We propose here a method for the construction of the Lewis and Riesenfeld time-dependent invariants. Instead of directly invoking the equation that defines the invariant associated with a time-dependent Hamiltonian, our method allows the step-by-step construction of the invariant as a product of operators, and mainly a straightforward derivation of its eigenvalue equation.