Abstract

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,p_i) (Q ⁱ, P_i), 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 P_idQⁱ = p_idqⁱ + 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.

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