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

δ-function strength

10

energy eigenvalue sign

-1

1

This Demonstration shows the spectrum of allowed wavenumbers

k

n

of a particle in a box with

δ

-potential as a function of its location. This spectrum determines the eigenmomenta

p

n

=

ℏk

n

and eigenenergies

E

n

=

2

p

n

2m

, respectively. Surprisingly, attractive and repulsive

δ

-potentials lead to degenerate (positive energy) spectra when the potential strength

|λ|

increases. The only difference in the two cases is a single negative-energy state that exists only for the attractive potential.