On Shtelen's Solution of the Free Linear Schrödinger Equation

DOI

10.2991/jnmp.1997.4.3-4.12How to use a DOI?

Abstract

The solution of the three-dimensional free Schrödinger equation due to W.M. Shtelen based on the invariance of this equation under the Lorentz Lie algebra so(1,3) of nonlocal transformations is considered. Various properties of this solution are examined, including its extension to n 3 spatial dimensions and its time decay; which is shown to be slower than that of the usual solution of this equation. These new solutions are then used to define certain mappings, Fn, on L2 (Rn ) and a number of their properties are studied; in particular, their global smoothing properties are considered. The differences between the behavior of Fn and that of analogous mappings constructed from usual solutions of the free Schrödinger equation are discussed.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - W.W. Zachary
PY  - 1997
DA  - 1997/09/01
TI  - On Shtelen's Solution of the Free Linear Schrödinger Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 377
EP  - 382
VL  - 4
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1997.4.3-4.12
DO  - 10.2991/jnmp.1997.4.3-4.12
ID  - Zachary1997
ER  -