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June  2018, 23(4): 1601-1621. doi: 10.3934/dcdsb.2018063

## Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations

 Department of Mathematics and Statistics, University of Nebraska Kearney, Kearney, Nebraska 68849, USA

* Corresponding author: Katherine A. Kime

Received  May 2017 Published  February 2018

We consider discrete potentials as controls in systems of finite difference equations which are discretizations of a 1-D Schrödinger equation. We give examples of palindromic potentials which have corresponding steerable initial-terminal pairs which are not mirror-symmetric. For a set of palindromic potentials, we show that the corresponding steerable pairs that satisfy a localization property are mirror-symmetric. We express the initial and terminal states in these pairs explicitly as scalar multiples of vector-valued functions of a parameter in the control.

Citation: Katherine A. Kime. Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1601-1621. doi: 10.3934/dcdsb.2018063
##### References:

show all references

##### References:
Example 1. $\alpha$-Localized, Mirror-Symmetric
Example 2. Not Localized, Not Mirror-Symmetric
Example 3. Localized with Equal Degree of Restriction Equal to 1, Not $\alpha$-Localized, Not Mirror-Symmetric
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