Bound-State Spectra for Two Delta Function Potentials

This Demonstration shows the bound-state spectra 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 .

Snapshot 1: typical symmetric and antisymmetric bound-state energies as a function of distance between the two attractive functions

Snapshot 2: for a weak potential strength , a second bound-state, the antisymmetric state, appears only when the distance between the two functions is large,

Snapshot 3: for a strong potential , the symmetric and antisymmetric states become degenerate when the distance between the two functions is increased