Revista mexicana de física
Print version ISSN 0035-001X
TORRES DEL CASTILLO, G.F.; BELLO MARTINEZ, H.; MEJIA SANCHEZ, R.J. and ZARATE PAZ, J.M.. Representation of canonical transformations in quantum mechanics. Rev. mex. fis. [online]. 2009, vol.55, n.2, pp. 134-139. ISSN 0035-001X.
The transformation of the wave functions induced by a given canonical transformation in the classical phase space, (qi,pi) (Q i, Pi), is considered. In the examples presented here, the kernel of the integral transform turns out to be essentially exp , where Λ (qi, Qi) is defined by PidQi = pidqi + dΛ. In the case of the time evolution, which is a canonical transformation, the kernel of the transform is the propagator, and is obtained directly by making use of the solution to the classical equations of motion.
Keywords : Wave functions; coordinate representation; canonical transformations; propagators.