# Bound-State Spectra for Two Delta Function Potentials

Bound-State Spectra for Two Delta Function Potentials

This Demonstration shows the bound-state spectra (d)of a particle of mass in the presence of two attractive potentials separated by a distance , . Since the Fourier transform of this potential is factorizable, , the bound-state spectra are easily obtained using the momentum-space Schrödinger equation. The energies are normalized to the magnitude of the symmetric-state energy at . Note that the second (antisymmetric) bound state appears only when the distance between the functions exceeds the critical value =2/λm.

E

b

m

δ

2d

V(x)=-λ[δ(x+d)+δ(x-d)]

V(k-k')=-2λcos((k-k')a)=-2λ[cos(ka)cos(k'a)+sin(ka)sin(k'a)]

d=0

δ

D

c

2

ℏ