The one dimensional infinite square well with variable mass
Abstract
We introduce a numerical method to obtain approximate eigenvalues for some problems of SturmLiouville type. As an application, we consider an infinite square well in one dimension in which the mass is a function of the position. Two situations are studied, one in which the mass is a differentiable function of the position depending on a parameter $b$. In the second one the mass is constant except for a discontinuity at some point. When the parameter $b$ goes to infinity, the function of the mass converges to the situation described in the second case. One shows that the energy levels vary very slowly with $b$ and that in the limit as $b$ goes to infinity, we recover the energy levels for the second situation.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5378
 Bibcode:
 2014arXiv1402.5378A
 Keywords:

 Quantum Physics;
 Mathematical Physics;
 34B24;
 65L15;
 81Q10
 EPrint:
 14 pages, 1 figure