| Abstract: | In this paper, we look for first integralsI(q;p;t) of time-dependent one-dimensional HamiltoniansH(q;p;t). We first present a formalism based on the use of canonical transformations, and it is seen thatI(q;p;t) can always be written in terms of two variablesI=P(u;v), whereu andv are functions ofq, p andt, without loss of generality. Moreover, it is shown that any Hamiltonian with first integralI(q;p;t) can be made autonomous in the space (u, v, T), whereT is a new time. On the other hand, the cases of a particle moving classically and relativistically in a time-dependent potentialV(q;t) are studied. In both cases, completely integrable potentials, together with the corresponding first integrals, are derived.CEA/CEV-M, BP7, 77181 Country, France, and CEA/CEN-S, SPEC, 91191, Gif sur Yvette Cédex, France. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 355–363, June, 1994. |
