The time-dependent Schr¨odinger equation is solved for a linear potential using operational methods; in particular, an extension of the Baker-Campbell-Hausdorff formula is exposed and used. Several initial conditions are considered. A closed formfor the Wigner function is presented. The results can be extended to the propagation of an electromagnetic field in the paraxial approximation.
Digital Object Identifier (DOI)
Soto-Eguibar, Francisco and M. Moya-Cessa, Héctor
"Solution of the Schr?dinger Equation for a Linear Potential using the Extended Baker-Campbell-Hausdorff Formula,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 23.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss1/23