The fourth eigenstate with V(x)=|x|.
The fourth eigenstate with V(x)=|x|.
The Schrödinger Numerov Eigensystem Model solves the time-independent Schrödinger Equation (a) with arbitrary potential energy V(x) using the Numerov method recast on a discrete lattice(b).
As shown by Pillai, Goglio, and Walker, the resulting matrix eigenvalue problem can be solved with just a few lines of code. In this model, we demonstrate how to do this computation in Java using the linear algebra package in the Apache Commons Math library.
Users can adjust the location of the hard hard walls at x-minimum and x-maximum and the potential V(x) in the region between the walls. The main window shows the potential and the energy eigenvalue spectrum along with a superimposed wave function psi. A second window shows the normalized wave function. The energy eigenvalue can be set by dragging the cursor in the main window or by entering the quantum number n.
The Schrödinger Numerov Eigensystem Model was developed by Wolfgang Christian using the Easy Java Simulations (EJS) version 4.3 authoring and modeling tool.
You can examine and modify a compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.