Particle-in-a-Box Spectra for Delta-Function Perturbation

This Demonstration shows the spectrum of allowed wavenumbers of a particle in a box with -potential as a function of its location. This spectrum determines the eigenmomenta and eigenenergies , respectively. Surprisingly, attractive and repulsive -potentials lead to degenerate (positive energy) spectra when the potential strength increases. The only difference in the two cases is a single negative-energy state that exists only for the attractive potential.