# On supersymmetric Dirac delta interactions

@article{Guilarte2014OnSD, title={On supersymmetric Dirac delta interactions}, author={J. M. Mateos Guilarte and J. M. Mu{\~n}oz Casta{\~n}eda and A. Moreno Mosquera}, journal={arXiv: Mathematical Physics}, year={2014} }

In this paper we construct $\mathcal{N}=2$ supersymmetric (SUSY) quantum mechanics over several configurations of Dirac-$\delta$ potentials from one single delta to a Dirac " comb \rq\rq. We show in detail how the building of supersymmetry on potentials with delta interactions placed in two or more points on the real line requires the inclusion of quasi-square wells. Therefore, the basic ingredient of a supersymmetric Hamiltonian containing two or more Dirac-$\delta$s is the singular potential…

## 4 Citations

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We present a detailed study of a generalised one-dimensional Kronig–Penney model using $$\delta \text {-}\delta '$$
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## References

SHOWING 1-10 OF 51 REFERENCES

### Quantum vacuum energies and Casimir forces between partially transparent $\delta$-function plates

- Physics
- 2013

In this paper the quantum vacuum energies induced by massive fluctuations of one real scalar field on a configuration of two partially transparent plates are analysed. The physical properties of the…

### Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D Dirac delta potential problem

- Physics
- 2008

### A new simple class of superpotentials in SUSY quantum mechanics

- Physics, Mathematics
- 2012

In this work, we introduce the class of quantum mechanics superpotentials W(x) = gε(x)x2n and study in detail the cases n = 0 and 1. The n = 0 superpotential is shown to lead to the known problem of…

### Self-isospectral periodic potentials and supersymmetric quantum mechanics

- Physics
- 1998

We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for {ital both} isospectral potentials to support zero modes, in…

### New solvable and quasi exactly solvable periodic potentials

- Physics
- 1999

Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specif- ically, the…

### On two-dimensional superpotentials: from classical Hamilton-Jacobi theory to 2D supersymmetric quantum mechanics

- Physics
- 2004

Superpotentials in J V = 2 supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system.…

### On the Supersymmetric Spectra of two Planar Integrable Quantum Systems

- Physics
- 2012

Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both systems…

### Vacuum energy in quantum field theory with external potentials concentrated on planes

- Physics
- 1992

In the presence of an idealized potential on two parallel planes represented by two one-dimensional delta -functions at x3=-d/2 and x3=+d/2 the authors discuss the Feynmann propagators for…