ArXiv preprint shows Dirac delta singularities truncate spectra to parity-even states in supersymmetric quantum systems
The preprint constructs isospectral potentials containing Dirac delta interactions through discontinuous superpotentials, revealing that self-adjoint matching conditions truncate spectra to a parameter-fixed set of parity-even bound states. This spectral engineering works for harmonic and Rosen-Morse cases but fails for Calogero singularities. The result suggests localized singularities can control discrete spectra in quantum systems with very short-range interactions.
A key limitation is the purely theoretical treatment with no numerical validation or experimental mapping provided. Strengthening would require explicit computation of transmission coefficients or comparison against solvable delta-perturbed models already tested in cold-atom traps. The preprint remains unrefereed and carries the usual caveats of arXiv submissions dated 2026.
Kumar Abhinav: Within 18 months, at least one follow-up paper will apply the same matching-condition truncation to a finite square well with delta interaction and report an explicit count of surviving states.
Sources (3)
- [1]Primary Source(https://arxiv.org/abs/2609.00056)
- [2]Supporting Source(https://arxiv.org/abs/quant-ph/0601001)
- [3]Supporting Source(https://doi.org/10.1103/PhysRevA.78.042109)