The Spline Potential Eigenfunctions Model computes the Schrödinger equation energy eigenvalues and eigenfunctions for a particle confined to a potential well with hard walls at -a/2 and a/2 and a smooth potential energy function between these walls.  The potential energy function is a third-order piecewise continuous polynomial (cubic spline) that connects N draggable control points.  Cubic-spline coefficients are chosen such that the resulting potential energy function and its first derivative is smooth throughout the interior and has zero curvature at the endpoints.  Users can vary the number of control points and can drag the control points to study level splitting in multi-well systems.  Additional windows show a table of energy eigenvalues and their corresponding energy eigenfunctions.

The Spline Potential Eigenfunctions Model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_qm_SplinePotentialEigenfunctions.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.6 of Java (JRE).