2004
Undergraduate Research Project:
Time
dependent Schrodinger equation: study of ionization in models
chosen to be both sufficiently simple and
important in applications.
You are invited to
follow our journey in mathematical
research.....
First steps:
The
problem is presented. Here are methods and results obtained for
somewhat similar problems.
But, of course, our
setting is different.
We make a plan.
We first need to understand the problem
very well. Let us first remember Laplace transform.
The simplest model of interest involves
delta-functions. We learned what they are,
and how to solve differential equations involving one delta-function.
First steps: solve the transformed
equation. And, in preparation for the next step,
read about Hilbert spaces, bounded and compact operators.
We worked a lot today. Let's relax
for a moment, distance ourselves from the details
and re-examine the problem from a broad perspective.
A few weeks later...
We made a lot of progress.
Here are some results:
We had to re-check some calculations...
I hope you had fun. We did.
On a more serious note: we are
preparing a paper to be submitted for publication.
Some links:
Michael Grabchak
Matt Kohut
Rodica D.
Costin
Ovidiu
Costin
2003 Undergraduate Research Project --- follow-up
The paper Rigorous
bounds of Stokes Constants for
some nonlinear ODEs at rank one
irregular singularities will appear in the journal Proceedings
of the Royal Society of London.
Click
here
to see the paper (.pdf)
Other links:
Page last modified 8/10/2004
