It is possible to obtain the interaction picture for a time-dependent Hamiltonian " H " 0, S ( " t " ) as well, but the exponentials need to be replaced by the unitary propagator for the evolution generated by " H " 0, S ( " t " ), or more explicitly with a time-ordered exponential integral.
12.
It is possible to obtain the interaction picture for a time-dependent Hamiltonian " H " 0, s ( " t " ) as well, but the exponentials need to be replaced by the unitary propagator for the evolution generated by " H " 0, s ( " t " ), or more explicitly with a time-ordered exponential integral.
13.
Where " s " is the transmissivity and storativity of the aquifer around the well ( m?/ s and unitless, respectively ), " r " is the distance from the pumping well to the point where the drawdown was observed ( m ), " t " is the time since pumping began ( seconds ), and " W ( u ) " is the " Well function " ( called the exponential integral, E 1, in non-hydrogeology literature ).
