P5870 - Modern Computational Methods in Solids

Spring 2011
Prof. Adrian E. Feiguin

Homework 1

Calculate the finite-difference matrix form for the square well. Using the same parameters as the example seen in class, diagonalize the Hamitonian and calculate the eigenvalues and eigenvectors. Use a range -10 &le x &le 10 and periodic boundary conditions. Consider different steps for the discretization and compare the first 10 eigenvalues and eigenstates.
The spectrum of the square well can be separated into bound and unbound states. Looking at the numerical solution: Do the unbound states form a continuum? Explain why.