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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
