system is small, interactions can be ignored (it is a Knudsen Gas $^{11}$), and multiplying the survival probability by the total number of particles gives us a quantitative value of mass inside the region. The second conclusion concerns the numerical significance. We have shown that the discretization developed by Arnold and Ehrhardt for the solution of open boundary prob- lems provides a viable numerical approach for solving the time dependent Schrodinger equation 8–10 when a constraint is suddenly removed. Although the present work consid- ers a one-dimensional model that is not sufficient to exhibit chaos, the code design forms the essential basis of future research on non-integrable, two-dimensional billiard models where chaos is present. The influence of chaos in these models will be explored by measuring the survival probability of particles in a trap with an open boundary. The results obtained with the code presented here show an excellent agreement with the analytic approach, offering reliability not only in the result obtained but also in the novel numerical method used. The success in the development of the numerical method opens up a reasonable extension to higher dimensional models. Also, it offers the possibility of understanding the quantum mechanical version of billiard models that experience classical chaotic behavior. In spite of the very low, by normal standards, temperature regime, a classical theoretical model was still adequate for the analysis of the Austin experiment. The quantum regime should also be accessible experimentally at yet lower, but still attainable, temperatures. Experimentalists are beginning to probe this regime. The authors benefitted from the suggestions of M. Ehrhardt, A. Arnold and K. Yawn, and the support of the division of Technology Resources at Texas Christian University. Acknowledgments 15 1 Oliver Knill,"Sinai billiard", <http://www.dynamical-systems.org/sinai/info.html>, (2000). 2 David M. Harrison,"Bunimovich stadium",<http://www.upscale.utoronto.ca/GeneralInterest /Harrison/Flash/Chaos/Bunimovich/Bunimovich.html>,(2006). 3 Eric W. Weisstein, "Billiards", <http://mathworld.wolfram.com/Billiards.html>,(2009).