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.



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Snapshot 1: nearly degenerate spectra for large potential strength,
Snapshot 2: dependence of negative-energy wavefunction size on the position of the -potential
Snapshot 3: for vanishing potential strength, the spectrum reduces to the well-known result
Analytical details underlying the Demonstration can be found at
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