- #1

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- TL;DR Summary
- Would a dense enough set of point interaction potentials around a particle keep it confined in a limited space?

Suppose I have a 3D polyhedron with a large number of faces, and put a repulsing Dirac delta potential, ##c\delta (\mathbf{x} - \mathbf{x}_i )## with ##c>0## at each vertex point ##\mathbf{x}_i## of the polyhedron. Could this kind of an arrangement of delta potentials keep a particle such as an electron trapped inside that polyhedral surface as a bound state, or would probability density leak out even with a really densely spaced set of Dirac deltas?

Where I got this idea is this recent MIT study about a possibility to keep neutron locked inside a quantum dot, despite it interacting only with the (highly localized) nuclei and not the electrons.

https://pubs.acs.org/doi/10.1021/acsnano.3c12929

A quantum dot is often modelled as a "particle in 2D or 3D box", so I would guess some kind of arrangement of point interaction potentials is how the neutron quantum dot would be described with a theoretical model, but I can't access the full text of that publication yet.

The problem I posed could be investigated with a numerical calculation by approximating the delta functions with sharp gaussian spikes, but that would be less time consuming with an equivalent 2D version.

Where I got this idea is this recent MIT study about a possibility to keep neutron locked inside a quantum dot, despite it interacting only with the (highly localized) nuclei and not the electrons.

https://pubs.acs.org/doi/10.1021/acsnano.3c12929

A quantum dot is often modelled as a "particle in 2D or 3D box", so I would guess some kind of arrangement of point interaction potentials is how the neutron quantum dot would be described with a theoretical model, but I can't access the full text of that publication yet.

The problem I posed could be investigated with a numerical calculation by approximating the delta functions with sharp gaussian spikes, but that would be less time consuming with an equivalent 2D version.