Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials

<p>In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound speed changes. This means the variable related to the sound speed is not constant. We will modify this variable so that it is piecewise constant. The specific operator in this equation also makes current time-stepping methods not practical. The method used here will apply an eigenfunction expansion technique used in previous research that eliminates the current time-stepping problems.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Year dc:date.available

2020

Author dc:creator

• Wright, Sarah

Contributors dc:contributor

• Dr. James V. Lambers
• Dr. Haiyan Tian
• Dr. Huiqing Zhu

• Partial Differential Equations
• Schrodinger Operators
• Numerical Analysis and Computation

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/785

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1838