Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials

Details Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials

1997-09-17

arxiv.org/abs/quant-ph/9709035v4

Physics Letters A243 (1998) 111-116

Physics

Quantum Physics

4 pages, ReVTeX double column format with an epsf figure, expanded references

Scientific paper

10.1016/S0375-9601(98)00188-1

It is shown that a potential consisting of three Dirac's delta functions on the line with disappearing distances can give rise to the discontinuity in wave functions with the proper renormalization of the delta function strength. This can be used as a building block, along with the usual Dirac's delta, to construct the most general three-parameter family of point interactions, which allow both discontinuity and asymmetry of the wave function, as the zero-size limit of self-adjoint local operators in one-dimensional quantum mechanics. Experimental realization of the Neumann boundary is discussed. KEYWORDS: point interaction, self-adjoint extension, $\delta'$ potential, wave function discontinuity, Neumann boundary PACS Nos: 3.65.-w, 11.10.Gh, 68.65+g

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