Their wave functions extend along the wall to infinity (not localized) and are not normalizable.
Kenji Ito, Masashi Naganuma, Hodaka Oda, Norisuke Sakai 2000, 'Nonnormalizable zero modes on BPS junctions', Nuclear Physics Bhttp://www.sciencedirect.com/science/article/pii/S0550321300004363. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The interaction potential gets completely regularized, which adds to the energy spectrum an infinite tower of previously non-normalizable states.
Francisco Correa, Olaf Lechtenfeld 2019, 'P T $$ \\mathcal{P}\\mathcal{T} $$ deformation of Calogero-Sutherland models', Journal of High Energy Physicshttp://link.springer.com/article/10.1007/JHEP05(2019)166. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)