Bound states for two delta potentials supported on parallel lines on the plane
DOI:
https://doi.org/10.33910/2687-153X-2022-3-1-37-42Keywords:
spectrum, variational approach, potential supported on lineAbstract
We consider a singular-potential supported on two parallel lines in R2 as a model of two interacting macromolecules. The intensity of the potential is constant, but each line contains a finite segment with a variation. Using variational approach, we study continuous and discrete spectra and estimate the gap between the eigenvalue and the continuous spectrum as a function of shift between the line segments. The existence of bound states for the system is proven by test function with separated variables.
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